The first part of the question is missing and it is:
A boat of mass 250 kg is coasting, with its engine in neutral, through the water at speed 3.00 m/s when it starts to rain. The rain is falling vertically, and it accumulates in the boat at the rate of 10.0 kg/hr.
Answer:
a(o) = 18.03 x 10^(-3) m/s^(-2)
Explanation:
First of all, if we make a momentum balance in the direction of motion (the x-direction), we'll discover that the change of the momentum will be equal to the forces acting on the boat.
Hence, there is only the drag force, which acts against the direction of motion as:
d(m·v)/dt = - k·v² (since f_d = - k·v²)
where k = 0.5 Ns²/m²
Now let's simplify the time derivative on the Left, by applying product rule of differentiation and we obtain:
v·dm/dt + m·dv/dt = - k·v²
where dm/dt = 10kg/hr (this is the change of the mass of the boat)
Furthermore, acceleration is the time derivative of time velocity, Thus;
a = dv/dt = - (k·v² + v·dm/dt) / m
Now, for the moment,when the rain starts; since we know all the values on the right hand side, let's solve for the acceleration ;
a(o) = - (ko·vo² + vo·dm/dt) / mo
= -[ (0.5(3)²) + (3x10/3600)/250
(dt = 3600secs because 1hr = 3600 secs)
So a(o) = 18.03 x 10^(-3) m/s^(-2)
Equipotentials are lines along which Select one: a. the electric field is constant in magnitude and direction. b. the electric charge is constant in magnitude and direction. c. maximum work against electrical forces is required to move a charge at constant speed. d. a charge may be moved at constant speed without work against electrical forces. e. charges move by themselves.
Answer:
option D is correct
Explanation:
It is important to note that equipotential lines are always perpendicular to electric field lines. No work is required to move a charge along an equipotential, since ΔV = 0. Thus the work is :
W = −ΔPE = −qΔV = 0.
Work is zero if force is perpendicular to motion. Force is in the same direction as E, so that motion along an equipotential must be perpendicular to E. More precisely, work is related to the electric field by:
W = Fd cos θ = qEd cos θ = 0.
- The change in kinetic energy Δ K.E by conservation should be:
Δ K.E = W
Since, W = 0:
Δ K.E = 0
- If change in kinetic energy is zero it means that charge moves at a constant speed. Hence, option D is correct.
Final answer:
Equipotential lines represent areas of constant electric potential, and moving a charge along these lines does not require work, as the potential difference is zero.
Explanation:
Equipotentials are lines that represent regions where the electric potential is constant. If we consider a charge at any point along an equipotential line, we can say that no work is required to move it along that line to another point. The correct answer to your question is option d: a charge may be moved at constant speed without work against electrical forces. This is because the potential difference (ΔV) between two points on the same equipotential line is zero, so the work done (ΔW = qΔV, where q is the charge) is also zero.
Equipotential lines are always perpendicular to electric field lines, and moving a charge from one equipotential line to another requires work as there is a change in potential. However, along an equipotential line, no such work is needed.
A telephone lineman is told to stretch the wire between two poles so the poles exert an 800Nforce on the wire. As the lineman does not have a scale to measure forces, he decides to measure the speed of a pulse created in the wire when he hits it with a wrench. The pulse travels 60m from one pole to the other and back again in 2.6s. The 60m wire has a mass of 15kg.a. Should the wire be tightened or loosened?b. Should the wire be tightened or loosened?
Answer:
The wire should be tightened because the present tension is 532.54 N where the required tension is 800 N and the higher the tension the more tightening is required.
Explanation:
To solve the question
v = [tex]\sqrt{\frac{F_t}{\mu} } = \sqrt{\frac{L*F_t}{m} }[/tex] where
v = velocity of the pulse in the string = 46.154 m/s
[tex]F_t[/tex] = Required tension force = 800 N
m = Mass of the wire = 15 kg
L = length of the wire to be tension-ed = 60 m
Since the pulse travels twice the distance of 60 m in 2.6 s the velocity is given by
v = 2×60/2.6 = 46.154 m/s
Therefore making [tex]F_t[/tex] the subject of the formula and substituting the values, we have
[tex]F_t[/tex] = [tex]\frac{v^2m}{L}[/tex] =[tex]\frac{46.154^{2*15} }{60}[/tex] = 532.54 N
This means that, as it is, the present tension in the wire is 532.54 N which is less than the required 800 N, therefore the wire should be tightened
The wire should be tightened because the current tension on the wire is less than the required tension.
The given parameters;
Required tension on the wire, T = 800 NDistance traveled by the Pulse, d = 60 mTime of motion of the pulse, t = 2.6 sMass of the wire, m = 15 kgThe speed of the wave as the pulse traveled from one pole to the other two times, is calculated as follows;
[tex]v = \frac{2d}{t} \\\\v = \frac{2 \times 60}{2.6} \\\\v = 46.154 \ m/s[/tex]
The tension created on the wire during the pulse motion is calculated as follows;
[tex]v = \sqrt{\frac{T}{m/L} } \\\\v ^2 = \frac{TL}{m} \\\\T = \frac{v^2 m}{L} \\\\T = \frac{(46.154)^2 \times 15}{60} \\\\T = 532.55 \ N[/tex]
The current tension on the wire (532.55 N) is less than the required tension of 800 N. Thus, the wire should be tightened.
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How much energy is evolved during the formation of 98.7 g of fe
Answer:
-852 KJ
Explanation:
[tex]Fe_{2}O_{3}(s)+2Al\rightarrow Al_{2}O_{3}+2Fe+\Delta H=-852KJ[/tex]
The above reaction is an exothermic reaction. Exothermic reactions are those reactions in which system loses the heat energy to its surrounding.
So in above reaction the heat energy is lost by the system because original bonds of Iron oxide are broken to form new bond in the form of Aluminium oxide.
Which of the following statements is true? there are only about 100 different kinds of atoms that combine to form all substances an atom is the smallest particle known to exist a large atom can be photographed with the aid of an ordinary microscope there are thousands of different kinds of atoms that account for a wide variety of substances none of the above
THE ANSWER IS : THERE ARE ONLY ABOUT 100 DIFFERENT KINDS OF ATOMS THAT COMBINE TO FORM ALL SUBSTANCES
Explanation:
To identify a diatomic gas (X2), a researcher carried out the following experiment: She weighed an empty 5.1-L bulb, then filled it with the gas at 1.00 atm and 20.0 ∘C and weighed it again. The difference in mass was 5.9 g . Identify the gas.
Answer: Nitrogen gas
Explanation:
Using ideal Gas's law
PV = nRT
where
Pressure of gas, P= 1atm
Volume of gas, V= 5.1L
no of moles of gas, n=
Ideal gas constant, R= 0.0821
Temperature of gas, T= 20°C = 20+273 = 293K
also, n= (mass/molar mass)
mass of the gas m = 5.9g
Molar mass of the gas = ?
So, PV = (mRT/M)
We're looking for molar mass M, then
M = mRT/PV
M = (5.9 * 0.0821 * 293)/(1 * 5.1)
M = 141.93/5.1
M = 27.8g/mol ~ 28g/mol
Since the gas is diatomic, then we say,
Atomic mass of gas = 1/2 * molar mass
Atomic mass = 1/2 * 28
Atomic mass = 14
Therefore, the gas is nitrogen.
A 3.1-mole sample of an ideal gas is gently heated at constant temperature 290 K. The gas expands to 1.5 times its initial volume as its pressure decreases. What is the change in the internal energy of the gas? Let the ideal-gas constant R = 8.314 J/(mol • K).
3000 J
1500 J
0 J
-3000 J
Answer:
0 J
Explanation:
In this process, we have an ideal gas gently heated at constant temperature.
The internal energy of an ideal gas is given by:
[tex]U=\frac{3}{2}nRT[/tex]
where
n is the number of moles of the gas
R is the gas constant
T is the absolute temperature of the gas
Therefore, the change in internal energy of a gas is given by
[tex]\Delta U=\frac{3}{2}nR\Delta T[/tex]
where [tex]\Delta T[/tex] is the change in temperature of the gas.
As we can see from the equation, the change in internal energy of an ideal gas depends only on the change in temperature.
In this problem, the temperature of the gas is constant:
T = 290 K
So the change in temperature is zero:
[tex]\Delta T=0[/tex]
Therefore, the change in internal energy is also zero.
Define what is vsepr theory?
Answer:
Valence shell electron pair repulsion theory
Explanation:
VSEPR stands for valence shell electron pair repulsion theory in which helps in predicting the geometric shape of a molecule based upon the number of lone pairs of electrons.It is also called the Gillespie-Nyholm theory after its two main discoverers, Ronald Gillespie and Ronald Nyholm.
In this theory the lone pair of atoms of the valence shell repel each other and attain such an angular position which minimizes the repulsion between the lone pair of electrons and the bonded pair of electrons so that it attains a stable state.This theory is however not related to the wave function and the orbital hybridization but is based only upon the electron density.[tex]\huge\mathcal{\underline{\underline{{ɑ}{\pmb{\sf{nswer \: : - }}}}}}[/tex]
[tex]\red:\implies[/tex][tex]\underline{\underline{\textbf{\pink{Valence Shell Electron Pair Repulsion \: : -}}}}[/tex]
The shape of molecule depend upon the number of valence shell electron pairs (bonded or nonbonded) around the central atom.Pairs of electron in the valence shelk repel one another since their electron clouds are negatively charged.These pairs of electron tend to occupy such positions in space that minimise repulsion and thus maximise distance between them.The valence shell is taken as sphere with the electrins pairs localising on the spherical surface at maximum distance from one another.A multiple bond is treated as if it is a single electron pair and the two or three electron pairs of a multiple bond are treated as a single auper pair.When two or more resonance structure can represent a molecule, the VSEPR model is applicable to any such structure.A 1.88-mole sample of an ideal gas is contracted at a constant temperature of 298 K. The initial volume is 24.5 L and the amount of work performed on it is 1040 J. What is the final volume? Let the ideal-gas constant R = 8.314 J/(mol • K).
20.2 L
19.6 L
22.5 L
30.6 L
Answer:
19.6 L
Explanation:
In an isothermal process, the temperature of the gas remains constant.
The work done on an ideal gas in an isothermal process is given by the equation:
[tex]W=-nRT ln\frac{V_f}{V_i}[/tex]
where
n is the number of moles
R is the gas constant
T is the temperature of the gas
[tex]V_i[/tex] is the initial volume
[tex]V_f[/tex] is the final volume
In this problem, we have:
W = 1040 J is the work done on the gas
n = 1.88 mol
T = 298 K is the gas temperature
[tex]V_i=24.5 L[/tex] is the initial volume
Solving the equation for Vf, we find the final volume:
[tex]V_f=V_i e^{-\frac{W}{nRT}}=(24.5)e^{-\frac{1040}{(1.88)(8.314)(298)}}=19.6 L[/tex]
Energy is measured in ___________. a. kilograms b. joules c. electron volts d. B or C Atoms and molecules are the fundamental building blocks of ___________. a. energy b. radiation c. matter d. gravity
Answer:
Energy is measured in JOULES.
Atoms and molecules are the fundamental building blocks of matter.
Explanation:
Matter is anything that has weight and occupies space. Locked within any given molecule or atom is some form of energy waiting to be activated. Energy can neither be created nor destroyed.
Two people, one of mass 78 kg and the other of mass 59 kg, sit in a rowboat of mass 88 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 2.9 m apart from each other, now exchange seats.
How far will the boat move?
Answer:
The boat moves 0.244 m towards the end where the 59 kg person was at the start of the calculations.
Explanation:
The boat only moves because the centre of mass changes a bit if the two people on opposite ends of the boat exchange seats.
The boat moves a distance of the change in centre of mass
Noting that the weight of the boat acts at the centre of the boat at 1.45m from both ends.
For convention, we call the original position of the 59 kg person as x=0
This means,
59 kg person is at x = 0 m
88 kg of the boat acts at x = 1.45 m from the end of the 59 kg person.
78 kg person is at x = 2.90 m
Centre of mass = X = (Σ mᵢxᵢ)/(Σ mᵢ)
For the initial setup,
X = [(59×0) + (88×1.45) + (78×2.90)]/(59+88+78)
X = (353.8/225)
X = 1.572 m
(Don't forget that this is 1.572 m from the end we designated x=0 m)
When the people exchange positions,
59 kg person is now at the other end of the boat with x = 2.90 m
88 kg of the boat still acts at the centre of the boat at x = 1.45 m
And 78 kg person is now at the end of the boat with x = 0 m
Centre of mass = X = (Σ mᵢxᵢ)/(Σ mᵢ)
X = [(59×2.90) + (88×1.45) + (78×0)]/(59+88+78)
X = (298.7/225)
X = 1.328 m
(This is 1.328 m from the end we designated x=0 m from the start)
So, the centre of mass moves a distance of (1.572 - 1.328) towards the end of the boat we designated x=0 m from the start.
Hence, the boat moves 0.244 m towards the end where the 59 kg person was at the start of the calculations.
Hope this Helps!!!
The maximum allowed rms current in a circuit before its circuit breaker trips is 12.5 A . If a maximum emf of 180 V is connected to a device whose resistance is 8.4 ohms, will the circuit breaker trip and interrupt the flow of electricity
Explanation:
The potential difference of 180 V is applied across resistance = 8.4 ohm
Thus the maximum current flowing I₀ = [tex]\frac{V}{R}[/tex] = [tex]\frac{180}{8.4}[/tex] = 21.4 A
The rms value of the current is = [tex]\frac{I_0}{\sqrt{2} }[/tex] = I₀ x 0.7 = 15 A
This value of current is greater than the 12.5 A . Thus the circuit will break .
Water molecules attracting other water molecules is called
Answer:
Water molecules attracting other water molecules is called cohesive attraction.
Explanation:
They are basically two forces in liquids that determine their wetting characteristics, they are cohesive and adhesive forces.
Cohesion is the attraction between molecules of same liquid example water and water, while adhesion is attraction between molecules of different liquids example alcohol and water.
Therefore, Water molecules attracting other water molecules is called cohesive attraction.
A little girl is going on the merry-go-round for the first time, and wants her 51 kg mother to stand next to her on the ride, 2.7 m from the merry-go-round's center. Part A If her mother's speed is 5.0 m/s when the ride is in motion, what is her angular momentum around the center of the merry-go-round
Answer:
686.70 kg m² / s
Explanation:
L= m * r²
= 51 * 2.7²
= 371.79 kg m²
w = v/r
= 5.0 m/s / 2.7 m
= 1.85 rev/sec
The momentum = I * w
= 371.79 * 1.85
= 686.70 kg m² / s
The angular momentum around the center of the merry-go-round is 686.70 kg m² / s
Calculation of the angular momentum:Since her mother who is 51 kg stand next to her on the ride, 2.7 m from the merry-go-round's center. And, the mother speed is 5.0 m/s.
So, the following formulas should be applied
L= m * r²
= 51 * 2.7²
= 371.79 kg m²
Now
w = v/r
= 5.0 m/s / 2.7 m
= 1.85 rev/sec
So finally
The momentum = I * w
= 371.79 * 1.85
= 686.70 kg m² / s
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A soccer ball kicked on a level field has an initial vertical velocity component of 15.0 mps. assuming the ball lands at the same height from which it was kicked was the total time of the ball in the air?
Answer:
The time taken for the ball to fly up in the air and back down again is 3.058 seconds.
Explanation:
Since the ball ends up at the same vertical distance ( on the ground) as it was at the start of its motion, we can set the total displacement of the ball equal to 0.
Thus, this problem can be simply solved by the following equation of motion:
[tex]s = u*t + \frac{1}{2} (a*t^2)[/tex]
Here, s = total change in distance = 0 m
u = initial speed = 15 m/s
a = acceleration due to gravity = -9.81 m/s^2
t = time (to be found)
Substituting these values in the equation we get:
[tex]0=15t+0.5(-9.81t^2)[/tex]
[tex]-15t = -4.905t^2[/tex]
[tex]t=15/4.905[/tex]
t = 3.058 seconds
So, the time taken for the ball to fly up in the air and back down again is 3.058 seconds.
A ball is thrown into the air with an initial velocity of 10 m/s at an angle of 45 degrees above the horizontal, as represented above. If air resistance is negligible the time needed for the ball to return to the ground is most nearly:_______.
Answer:
1.44 s
Explanation:
Since it is a projectile motion, we use the formula for the total time of flight,t
t = 2Usinθ/g where U = initial velocity of ball = 10 m/s, θ = 45 and g = 9.8 m/s²
t = 2Usinθ/g = 2 × 10sin45/9.8 = 1.44 s
So, the time needed for the ball to return to the ground is most nearly: 1.44 s
We have that for the Question it can be said that the time needed for the ball to return to the ground is most nearly
T=1.44
From the question we are told
A ball is thrown into the air with an initial velocity of 10 m/s at an angle of 45 degrees above the horizontal, as represented above. If air resistance is negligible the time needed for the ball to return to the ground is most nearly
Generally the Newton's equation for the vertical displacement is mathematically given as
[tex]y=ut+1/2at^2\\\\Therefore\\\\T=\frac{2Usin\theta}{g}\\\\T=\frac{2*10*sin45}{9.8}\\\\[/tex]
T=1.44
Therefore
the time needed for the ball to return to the ground is most nearly
T=1.44
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The key difference between the binomial and hypergeometric distribution is that
Explanation:
Both distributions describe the number of times an event occurs in a givn number of trials. In the binomial distribution, the probability is the same for each trial. While in the hypergeometric distribution, each trial changes the probability of each subsequent trial, since there is no replacement.
If a flask initially contains 1.0 atm of A and 1.2 atm of B, what is the pressure in the flask if the reaction proceeds to completion? (Assume constant volume and temperature.) If a flask initially contains 1.0 of and 1.2 of , what is the pressure in the flask if the reaction proceeds to completion? (Assume constant volume and temperature.) 3.2 atm 2.2 atm 1.7 atm 1.2 atm
Answer:
Explanation:
According to Dalton's partial pressure law, the total pressure of a mixture of gases is the sum of the individual pressure of the gases that make up the mixture. Mathematically;
[tex]P_total = P_1 + P_2 + ...... + P_n[/tex]
In this case;
[tex]P_{total} = P_A + P_B[/tex]
1. 0 + 1.2 = 2.2 atm.
The correct answer is 2.2 atm.
The pressure in the flask when the reaction proceeds to completion is 2.2 atm.
Explanation:
In this question, we are given the initial pressures of two gases, A and B, in a flask. The question asks us to determine the pressure in the flask if the reaction proceeds to completion, assuming constant volume and temperature.
When two gases react, they combine to form a new gas or gases. Since the volume and temperature are constant, the total number of moles of gas in the flask remains the same. According to Dalton's law of partial pressures, the pressure of the gases in the flask is equal to the sum of the pressures each gas would exert if it occupied the flask alone. Therefore, if the reaction proceeds to completion, the pressure in the flask would still be the sum of the initial pressures of gases A and B, which is 1.0 atm + 1.2 atm = 2.2 atm.
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Consider the system shown in the figure. Block A has weight 4.91 N and block B has weight 2.94 N. Once block B is set into downward motion, it descends at a constant speed. Assume that the mass and friction of the pulley are negligible.
Calculate the coefficient of kinetic friction mu between block A and the table top.
I'm not sure where to begin.
Answer:
Explanation:
Check attachment for solution
The coefficient of kinetic friction between block A and the tabletop is obtained to be 0.6.
Two-body ProblemThis problem can be analysed using the free body diagram of the two blocks. (Diagrams given as attachment.)
Consider the block 'B'. It descends at a constant speed. It has only vertical motion.Also given, [tex]W_B=2.94\,N[/tex]According to Newton's second law;
[tex]\sum F=ma[/tex]Here, a = 0 m/s, therefore;
[tex]T-W_B=0[/tex][tex]\implies T = W_B = 2.94\,N[/tex]Block A has a weight, [tex]W_A = 4.91N[/tex]Now, consider the vertical forces in the case of block A.
The box has no vertical motion.
So, from Newton's second law;
[tex]\sum F=ma[/tex][tex]N-W_A=0[/tex][tex]\implies N=W_A=4.91\,N[/tex]Now, consider the horizontal forces in the case of block A.
Here also the acceleration of the block is zero.
So, from Newton's second law;
[tex]\sum F=ma[/tex][tex]T-F_{fr}=0[/tex][tex]F_{fr}=T=2.94\,N[/tex]But frictional force is given by;
[tex]F_{fr}= \mu _k N[/tex][tex]\implies \mu _k= \frac{F_{fr}}{N} =\frac{2.94}{4.91}=0.598[/tex][tex]\therefore \mu _k \approx 0.6[/tex]
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Even when you have the right-of-way, you're responsible for _____ before you drive forward.
A. waving to other road users
B. honking to alert other road users
C. making sure the path is clear
D. flashing your headlights
Answer:c, making sure the path is clear.
Explanation: i got it right :)
When you have the right-of-way, you're responsible for making sure the path is clear before you drive forward.
Explanation:Even when you have the right-of-way, you're responsible for making sure the path is clear before you drive forward. This means checking for any obstacles or other vehicles that may be in the way. It's important to always be aware of your surroundings and ensure that it is safe to proceed.
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(a) As a soap bubble thins it becomes dark, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes dark when the path length difference is less than one-fourth the wavelength, what is the thickest the bubble can be and appear dark at all visible wavelengths? Assume the same index of refraction as water. (b) Discuss the fragility of the film considering the thickness found
Answer:
t< 75 nm
Explanation:
A soap bubble is a thin film where when the beam enters the film it has a 180º phase change due to the refractive index and the wavelength changes between
λ = λ₀ / n
In the case of constructive interference in the curve of the spherical film it is
2 nt = (m + ½) λ₀
Where t is the thickness of the film and n the refractive index that does not indicate that we use that of water n = 1.33, m is an integer. The thickness of the film for the first interference (m = 0) is
t = λ₀ / 4 n
A thickness less than this gives destructive interference.
Let's look for the thickness for the visible spectrum
Violet light λ₀ = 400 nm = 400 10⁻⁹ m
t₁ = 400 10⁻⁹ / 4 1.33
t₁ = 75.2 10-9 m
Red light λ₀ = 700 nm = 700 10⁻⁹ m
t₂ = 700 10⁻⁹ / 4 1.33
t₂ = 131.6 10⁻⁹ m
Therefore, for all wavelengths to have destructive interference, the thickness must be less than 75 10⁻⁹ m = 75 nm
b) a film like eta is very thin, it is achieved when gravity thins the pomp, but any movement or burst of air breaks it,
The maximum thickness for a soap bubble to appear dark at all visible wavelengths is 50 nm; this correlates with increased fragility due to the thinness of the film.
Explanation:When analyzing thin film interference, specifically in a soap bubble, we look for conditions that lead to darkness due to destructive interference. The soap bubble appears dark when the path length difference is less than one-quarter of the wavelength of light, assuming an index of refraction similar to water. As the visible light spectrum ranges from about 400 nm (violet) to 700 nm (red), we use the shortest wavelength to ensure darkness across all visible wavelengths. Therefore, the maximum thickness (t) is:
The thickest the bubble can be and appear dark at all visible wavelengths is 50 nm. Fragility of the film correlates highly with thinness, as such a minuscule thickness is highly susceptible to rupture from minimal force or even a slight change in surface tension.
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Typically a Switch operates at layer 2 of the OSI model. However, small organizations, such as a SOHO, can purchase a switch that also interprets Layer 3 data and works much like a router. What is this device called
Answer:
Layer 3 switch.
Explanation:
A layer 3 switch carrys out both the function of a switch and a router. It acts as a switch that links all the devices that are on the same subnet or virtual LAN at lightning speeds and has IP routing intelligence built into it to carry out the function of a router. It can support routing protocols, check incoming packets, and can also carry out routing decisions based on the source and the destination addresses.
The sound source of a ship's sonar system operates at a frequency of 18.0 kHzkHz . The speed of sound in water (assumed to be at a uniform 20∘C)∘C) is 1482 m/sm/s. The ship is at rest in the water.
(a) What is the wavelength of the waves emitted by the source?
(b) What is the difference in frequency between the directly radiated waves and the waves reflected from a whale traveling directly toward the ship at 4.95 m/s? The ship is at rest in the water.
The wavelength of the waves emitted by the source is 0.082 m or 8.2 cm. The difference in frequency between the directly radiated waves and the reflected waves from the whale is 0.012 kHz or 12 Hz.
Explanation:(a) We can find the wavelength of the waves emitted by the source using the formula: Speed = Frequency × Wavelength. We have the speed of sound in water as 1482 m/s and the frequency as 18.0 kHz (which is equal to 18000 Hz). Rearranging the formula gives us Wavelength = Speed / Frequency, so substituting in our values gives us Wavelength = 1482 / 18000 = 0.082 meters or 8.2 cm.
(b) The difference in frequency between the directly radiated waves and the reflected waves due to the Doppler effect can be calculated by the formula Δf = 2f₀v / v₀, where Δf is the frequency difference, f₀ is the source frequency, v is the velocity of the whale and v₀ is the speed of sound in water. Substituting in gives us Δf = 2(18.0 kHz)(4.95 m/s) / 1482 m/s = 0.012 kHz or 12 Hz.
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A person in the passenger basket of a hot-air balloon throws a ball horizontally outward from the basket with a speed of 10.0 m/s. What initial velocity (magnitude and direction) does the ball have relative to a person standing on the ground if the hot-air balloon is rising at 6.0 m/s relative to the ground during this throw?
Answer:
Explanation:
Given
balloon is rising with a speed of [tex]u_y=6\ m/s[/tex]
Person throws a ball out of basket with a horizontal velocity of [tex]u_x=10\ m/s[/tex]
Considering upward direction to be positive
When ball is thrown it has two velocity i.e. in upward direction and in horizontal direction so net velocity is
[tex]v_{net}=\sqrt{(u_x)^2+(u_y)^2}[/tex]
[tex]v_{net}=\sqrt{(6)^2+(10)^2}[/tex]
[tex]v_{net}=\sqrt{36+100}[/tex]
[tex]v_{net}=\sqrt{136}[/tex]
[tex]v_{net}=11.66\ m/s[/tex]
Direction of velocity
[tex]\tan \theta =\dfrac{u_y}{u_x}[/tex]
[tex]\tan \theta =\dfrac{6}{10}[/tex]
[tex]\theta =30.96^{\circ}[/tex]
where [tex]\theta [/tex] is angle made by net velocity with horizontal .
A type of light bulb is labeled having an average lifetime of 1000 hours. It’s reasonable to model the probability of failure of these bulbs by an exponential density function with mean µ = 1000. Use this model to find the probability that a bulb fails within the first 300 hours.
Answer:
[tex]0.2592 \ or \ 25.92\%[/tex]
Explanation:
The exponential density function is given as
[tex]f(t)=\left \{ {{0} \atop {ce^{ct}}} \right\\0,t<0\\ce^{ct},t\geq 0[/tex]
[tex]\mu=\frac{1}{c}\\c=\frac{1}{\mu}\\\\=\frac{1}{1000}=0.001\\\\f(t)=0.001e^{-0.001t}[/tex]
To find probability that bulb fails with the first 300hrs, we integrate from o to 300:
[tex]P(0\leq X\leq 300)=\int\limits^{300}_0 {f(t)} \, dt\\\\=\int\limits^{300}_0 {0.001e^{-001t}} \, dt\\ =|-e^{-0.001t}| \ 0\leq t\leq 300[/tex]
[tex]P(0\leq X\leq 300)=-0.7408+1\\=0.2592[/tex]
Hence probability of bulb failing within 300hrs is 25.92% or 0.2592
An electric vehicle starts from rest and accelerates at a rate of1.9m/s2in a straight line until it reaches a speed of23m/s. The vehicle then slows at a constant rate of 1.4m/s2 until it stops.(a)How much time elapses from start to stop
Answer: 10.53 seconds
Explanation:
in the attachment
Explanation:
Below is an attachment containing the solution.
A 12.0-g bullet is fired horizontally into a 109-g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having spring constant 152 N/m. The bullet becomes embedded in the block. If the bullet-block system compresses the spring by a maximum of 78.0 cm, what was the speed of the bullet at impact with the block?
Answer:
v₀ = 280.6 m / s
Explanation:
we have the shock between the bullet and the block that we can work with at the moment and another part where the assembly (bullet + block) compresses a spring, which we can work with mechanical energy,
We write the mechanical energy when the shock has passed the bodies
Em₀ = K = ½ (m + M) v²
We write the mechanical energy when the spring is in maximum compression
[tex]Em_{f} = K_{e} \\= \frac{1}{2} kx^2\\ Em_0 = Em_{f}[/tex]
½ (m + M) v² = ½ k x²
Let's calculate the system speed
v = √ [k x² / (m + M)]
v = √[152 ×0.78² / (0.012 +0.109) ]
v = 27.65 m / s
This is the speed of the bullet + Block system
Now let's use the moment to solve the shock
Before the crash
p₀ = m v₀
After the crash
[tex]p_{f} = (m + M) v[/tex]
The system is formed by the bullet and block assembly, so the forces during the crash are internal and the moment is preserved
[tex]p_0 = p_{f}[/tex]
m v₀ = (m + M) v
v₀ = v (m + M) / m
let's calculate
v₀ = 27.83 (0.012 +0.109) /0.012
v₀ = 280.6 m / s
Which changes would cause the fusion rate in the sun’s core to increase?
Answer:
Explanation
There are two factors that can cause the fusion rate in the sun's core to increase.
1) Rise in the temperature of core:
If the temperature of the sun's core increases then it will increases the nuclear fusion reaction. The nuclear fusion reactions has such a strong dependency on temperature that even a smallest rise in temperature will results in the higher rate of reaction. That is why these reactions happen in the hottest core of the stars.
2) Reduction in the radius of the core:
Density plays a huge role in the nuclear fusion reactions. If the radius of the sun's core decrease then there will be an increase in the density of the core. Thus the gravitational pressure will also increases. In order to resist this increase in pressure the fusion reactions will speed up and their rate becomes higher.
The wavelength of red light is about 700 nm: λred = 700 nm. Which is larger, a grain of sand (diameter roughly 0.2 mm) or a wave of red light? How many times larger?
Answer:
The grain of sand is larger by a factor of about 286.
Explanation:
We express both values in standard form in the SI unit of metre so that the comparison can be easily done:
[tex]\lambda_R = 700 \text{ nm} = 700 \times 10^{-9} \text{ m} = 7\times10^{-7} \text{ m}[/tex]
Diameter of grain of sand = [tex]0.2 \times \text{ mm} = 0.2\times10^{-3}\text{ m} = 2\times10^{-4}\text{ m}[/tex]
It is seen that the grain of sand is larger.
The ratio of the sizes is given by
[tex]\dfrac{2\times10^{-4} \text{ m}}{7\times10^{-7} \text{ m}}=286[/tex]
Which was the most important effect of the bessemer process
Answer: The effect of Bessemer process is its reduction in cost for steel production.
Explanation:
In the manufacturing of steel, Bessemer process was the first method discovered for mass production of steel. This was discovered by Sir Henry Bessemer and Williams Kelly both from United States. This method aids in the removal of impurities from iron and converts it to steel in few minutes (this usually takes a full day to achieve). The economy of the country improved as steel was made faster and cheaper causing companies to build thousands of new railroads.
A circular curve of highway is designed for traffic moving at 60 km/h. Assume the traffic consists of cars without negative lift. (a) If the radius of the curve is 150 m, what is the correct angle of banking of the road? (b) If the curve were not banked, what would be the minimum coefficient of friction between tires and road that would keep traffic from skidding out of the turn when traveling at 60 km/h?
Answer:
a) 10.7° ≈ 11°
b) 0.19
Explanation:
If the road is banked at an angle, without seeking the help of friction, (i.e. frictionless road), the forces acting on the car are shown in the attached free body diagram to the question
In the y - direction
mg = N cos θ (eqn 1)
mg = weight of the car.
N = normal reaction of the plane on the car
And in the direction parallel to the inclined plane,
(mv²/r) = N sin θ (eqn 2)
(mv²/r) = force keeping the car in circular motion
Divide (eqn 2) by (eqn 1)
(v²/gr) = Tan θ
v = velocity of car = 60 km/h = 16.667 m/s
g = acceleration due to gravity
r = 150 m
(16.667²/(9.8×150)) = Tan θ
θ = Tan⁻¹ (0.18896)
θ = 10.7° ≈ 11°
b) In the absence of banking, the frictional force on the road has to balance the force keeping the car in circular motion
That is,
Fr = (mv²/r)
Fr = μN = μ mg
μ mg = mv²/r
μ = (v²/gr) = (16.667²/(9.8×150)) = 0.19
Hope this Helps!!!