1. Our entire solar system orbits around the center of the Milky Way Galaxyabout once every 230 million years.
2. The Milky Way and Andromeda galaxies are among a few dozen galaxies that make up our Local Group.
3. The Sun appears to rise and set in our sky because Earth orbitsonce each day.
4. You are one year older each time Earth rotatesabout the Sun.
5. On average, galaxies are getting farther apart with time, which is why we say our universeis expanding.
6. Our solar systemis moving toward the star Vega at about 70,000 km/hr.

Answer:

Part A:

[tex]Displacement\ vector= -40\hat i+20\hat j+25\hat k[/tex]

Part B:

Magnitude of displacement=44.721359 m

Explanation:

Given Data:

40 m in negative direction of the x axis

20 m perpendicular path to his left (considering +ve y direction)

25 m up a tower (Considering +ve z direction)

Required:

Solution:

Part A:

[tex]Displacement= (0-40)\hat i+(0+20)\hat j+(0+25)\hat k\\Displacement= -40\hat i+20\hat j+25\hat k[/tex]

where:

i,j,k are unit vectors

Part B:

Sign falls to foot of tower so z=0

[tex]Displacement= -40\hat i+20\hat j+0\hat k[/tex]

Magnitude of displacement:

[tex]Magnitude\ of\ displacement=\sqrt{(-40)^2+(20)^2+0^2} \\Magnitude\ of\ displacement=44.721359\ m[/tex]

Answer:

5.8×10^11Hz

Explanation:

Frequency is the ratio of the speed of the light wave to its wavelength.

Frequency (f)= velocity(v)/Wavelength (¶)

Given wavelength = 5.2×10^-5cm = 5.2×10^-3m (converted to meters)

Velocity of light = 3×10^8

Substituting the values given in the formula we have

Frequency = 3×10^8/ 5.2×10^-3

Frequency = 5.8×10^11Hz

The frequency of the green light from the traffic signal is 5.77 × 10¹⁴ Hertz.

Given the data in the question;

Wavelength; [tex]\lambda = 5.20*10^{-5}cm = 5.20*10^{-7}m[/tex]

Frequency; [tex]f = \ ?[/tex]

To determine the frequency of the green light, we use the expression for the relations between wavelength, frequency and speed of light.

[tex]\lambda = \frac{c}{f} \\[/tex]

Where [tex]\lambda[/tex] is wavelength, f is frequency and c is speed constant ([tex]3* 10^8m/s[/tex])

We substitute the values into the equation

[tex]5.20*10^{-7}m = \frac{3*10^8m/s^}{f} \\\\f = \frac{3*10^8m/s^}{5.20*10^{-7}m}\\\\f = 5.77 * 10^{14}s^{-1}\\\\f = 5.77 * 10^{14}Hz[/tex]

Therefore, the frequency of the green light from the traffic signal is 5.77 × 10¹⁴ Hertz.

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The magnitude of the position vector :r is approximately 7.32 m. When the centripetal acceleration is directed due east, :r will also be due east. When the centripetal acceleration is directed due south, :r will also be due south.

The magnitude of the position vector :r can be determined using the equation :a = :v^2 / r where :v is the speed of the man and :a is the centripetal acceleration. Rearranging the equation, we get :r = :v^2 / :a. Substituting the given values, we find :r = (3.66^2) / 1.83 which is approximately 7.32 m.

When the centripetal acceleration is directed due east, the position vector :r will be due east. When the centripetal acceleration is directed due south, the position vector :r will be due south.

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Answer:

t = 2.5 hours

Explanation:

given,

speed of the bike for t time= 18 mi/h

final speed of the bike after t time = 12 mi/h

total distance, D = 69 miles

total time, T= 4.5 hour

time for which speed of the bike is 18 mi/h = ?

we know distance = speed x time

now,

18 x t + 12 (4.5 - t) = 69

6 t + 54 = 69

6 t = 15

t = 2.5 hours

The bike was at the speed of 18 mi/h for 2.5 hours.

Answer:

50 V / 150 V

Explanation:

Final answer:

The question discusses the grounding of a transformer based on voltage levels and defines the characteristics of step-down and step-up transformers in terms of voltage and current. Transforming the power efficiently is crucial, and the number of windings plays a significant role in determining the output voltage and current.

Explanation:

The question pertains to transformers and their operating principles regarding voltage, current, and the number of windings. If the voltage at the secondary side of a transformer is less than 50 volts and the primary side exceeds 150 volts to ground, the secondary side shall be grounded.

When a transformer has fewer windings in the secondary coil compared to the primary coil, it is a step-down transformer, meaning the secondary voltage is less than the primary voltage. Conversely, a step-up transformer has more windings in the secondary coil, resulting in a higher secondary voltage compared to the primary voltage.

In the context of primary and secondary properties of transformers, option (a) the Primary voltage is higher than secondary voltage defines a step-down transformer. Additionally, (c) the Primary current is higher than secondary current is not typically true for a step-down transformer.

Instead, the primary current would be lower than the secondary current since power (P = IV) is conserved across the transformer. Therefore, if the voltage decreases, the current must increase to maintain the equivalent power (assuming ideal conditions with no power losses).

Answer:

The angular diameter is 77.35 arc-seconds.

Explanation:

The angular diameter, as shown in the figure, is the angle [tex]x[/tex]  subtended by the the diameter of the object.

Before we do the calculation, we first convert everything to meters.

The diameter of the of the object in meters is

75cm =0.75m,

and the distance to the object in meters is

2 km = 2000 m.

Now, from trigonometry we get:

[tex]tan (\frac{x}{2} )= \dfrac{radius}{length} = \dfrac{0.75/2}{2000} \\\\\dfrac{x}{2} = tan^{-1}(\dfrac{0.75/2}{2000})\\\\\dfrac{x}{2}= 0.0107\\\\\boxed{x= 0.0215^o}[/tex]

and since 1 degree = 3600 arc-seconds, [tex]x[/tex] in arc-seconds is

[tex]x= 0.0215*3600 \\\\\boxed{x= 77.35''}[/tex]

Answer:

See attachment below

Explanation:

The normal force exerted on the car by the curved road is 13,139.7 N.

The radial acceleration of the car is 6.56 m/s².

The speed of the car is 21.43 m/s.

In the case of a banked curve with friction, the centripetal acceleration is increased by normal force and frictional force since it prevents the car from skidding.

The given parameters;

The normal force exerted on the car by the curved road is calculated as follows;

[tex]\Sigma F_y = 0\\\\Ncos(\theta) - \mu_s Nsin(\theta) - mg = 0\\\\Ncos(\theta) - \mu_s Nsin(\theta) = mg\\\\N(cos\theta \ - \ \mu_s sin(\theta)) = mg\\\\N = \frac{mg }{cos\theta - \mu_s sin(\theta)} \\\\N = \frac{(1200 \times 9.8)}{cos (12) - \ 0.4\times sin(12)} \\\\N = 13,139.7 \ N[/tex]

The radial acceleration of the car is calculated as follows;

[tex]\Sigma F_x = ma_c\\\\ma_c = Nsin(\theta) + \mu_s N cos(\theta)\\\\a_c = \frac{Nsin(\theta) + \mu_s N cos(\theta)}{m} \\\\a_c = \frac{(13, 139.7)sin(12) \ + \ 0.4 \times 13,139.7cos(12)}{1200} \\\\a_c = 6.56 \ m/s^2[/tex]

The car's speed is calculated as follows;

[tex]a_c = \frac{v^2}{r} \\\\v^2 = a_c r\\\\v = \sqrt{a_c r} \\\\v = \sqrt{6.56 \times 70} \\\\v = 21.43 \ m/s[/tex]

In the case of a banked curve with friction, the centripetal acceleration is increased by the following;

[tex]ma_c = Nsin(\theta) + F_s\\\\ma_c = Nsin(\theta) + \mu_s Ncos (\theta)[/tex]

where;

Thus, In the case of a banked curve with friction, the centripetal acceleration is increased by normal force and frictional force since it prevents the car from skidding.

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The correct options are V, W, and Y

Uniform Circular Motion is the motion when an object moves in a circular path with constant speed (uniform speed). In such a motion,

1- The position keeps on changing,

2- The speed remains constant

Now checking all the option

V- It shows the uniform circular motion since all the direction is uniform,

W-It shows the uniform circular motion since all the direction is uniform,

X-Direction are different,

Y-It shows the uniform circular motion since all the direction is uniform,

Hence, all the above options,

The correct options are V, W, and Y

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Answer:

272.56 or 271.44

Explanation:

[tex]Fbeat=\frac{1}{Tbeat} \\=\frac{1}{1.8} \\=0.56 Hz[/tex]

[tex]Fbeat=abs(f1-f2)\\0.56=abs(272-f2)\\\\f2=272.56\\f2=271.44[/tex]

Energy level transitions in physics occur when an atom or molecule absorbs or emits electromagnetic radiation. The circumstances of these transitions depend on the system being studied.

Energy level transitions in physics typically occur when an atom or a molecule absorbs or emits electromagnetic radiation. When an electron within an atom moves from a lower energy level to a higher energy level, it absorbs energy. Conversely, when an electron moves from a higher energy level to a lower energy level, it emits energy in the form of electromagnetic radiation.

These transitions can occur under various circumstances, such as when an atom is excited by heat or light, or when an electron interacts with another particle. For example, in the hydrogen atom, transitions between different energy levels give rise to the absorption and emission of specific wavelengths of light, leading to the existence of discrete spectral lines. It is important to note that the exact circumstances of energy level transitions depend on the specific system being studied, such as atoms, molecules, or subatomic particles.

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Energy level transitions in atoms occur when an electron absorbs or emits energy, typically through photon interactions, due to electronic rearrangements.

Energy level transitions in atoms happen when electrons change their energy states. These transitions can occur under several circumstances:

Absorption of Photons: Electrons can move to higher energy levels by absorbing photons with specific energy levels corresponding to the energy difference between the levels. This is observed in absorption spectra.

Emission of Photons: Electrons release energy in the form of photons when transitioning from higher to lower energy levels. These emitted photons produce emission spectra.

Electron Collisions: In certain situations, such as in a plasma, collisions between electrons and other particles can excite electrons to higher energy states, leading to subsequent de-excitation and photon emission.

External Energy Sources: External sources like electrical discharges or high-temperature environments can energize electrons, causing transitions between energy levels.

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Answer:

1) False

2) False (chemical, thermal, mechanical and electrical)

3) False

Explanation:

1.

We have the expression for the root mean square velocity of the molecules of gases as:

[tex]v_{rms}=\sqrt{\frac{3.k_b.T}{M} }[/tex]

where:

[tex]k_b=[/tex] Boltzmann constant

[tex]T=[/tex] temperature of the gas

[tex]M=[/tex] molecular mass of the gas

2.

In a coal-fired powered the types of energy form start to finish can be given as;

3.

In a coal fired power plant the approximate percentage of original energy in the coal lost to heat is approximately 60%.

Answer:

[tex]2.044 * 10^{-18}[/tex] J

Explanation:

Parameters given:

[tex]n_{1} = 4\\\\n_{2} = 1[/tex]

We know that the electron fell from level 4 to level 1. We can use the Rydberg's equation to find the [tex]2.044 * 10^{-18}[/tex] that is emitted by the electron in the process. Rydberg's equation is given as:

1/λ = [tex]R * (\frac{1}{(n_{2})^2} - \frac{1}{(n_{1})^2})[/tex]

where R = Rydberg's constant = [tex]1.0973731568508 * 10^{7}[/tex]

1/λ =    [tex]1.0973731568508 * 10^{7} (\frac{1}{1^{2}} - \frac{1}{4^{2}} } )[/tex]

1/λ =    [tex]1.0973731568508 * 10^{7} (\frac{1}{1} - \frac{1}{16} } )[/tex]

1/λ =   [tex]1.0973731568508 * 10^{7} * \frac{15}{16}[/tex]

1/λ =   [tex]1.029 * 10^{7}[/tex] [tex]m^{-1}[/tex]

∴ λ = [tex]9.72 * 10^{-8}[/tex] m

Energy of the photon is given by:

E = (hc)/λ

where

h = Planck's constant = [tex]6.62607004 * 10^{-34} m^2 kg / s[/tex]

c = speed of light = 299792458 m / s

∴ E =    [tex]\frac{6.62607004 * 10^{-34} * 299792458}{9.72 * 10^{-8}}[/tex]

E = [tex]2.044 * 10^{-18}[/tex] J

The energy of the photon is [tex]2.044 * 10^{-18}[/tex] J

Final answer:

The energy of a photon emitted when an electron in a hydrogen atom falls from n=4 to n=3 can be found using the Rydberg formula. The constant R (Rydberg constant) along with the energy levels n1 and n2 are used in the formula to calculate this energy in joules.

Explanation:

The magnitude of energy of a photon of light that is emitted when an excited electron in a hydrogen atom falls from n = 4 to n = 3 can be calculated using the Rydberg formula for the energy difference between two hydrogen energy levels. In this case, since the question only specifies a drop of one energy level, we'll correct the typo where it currently indicates a fall from n=4 to n=1, and we'll proceed with the fall from n=4 to n=3. The formula to use is:

E = R ×  (1/n1² - 1/n2²)

where:

R is the Rydberg constant (2.179 × 10⁻¹⁸ J),

n1 and n2 are the principal quantum numbers (integers) for the initial and final energy levels, respectively.

The calculation is then:

E = 2.179 × 10⁻¹⁸ J ×  (1/3² - 1/4²) = 2.179 × 10⁻¹⁸ J ×  (1/9 - 1/16) = 2.179 × 10⁻¹⁸ J × (7/144)

After calculating the above expression, you will get the energy in joules of the photon emitted due to the electron's transition.

Answer:

D) Sound waves carry energy parallel to the motion of the wave, while light waves carry energy perpendicular to it.

Explanation:

A) This is incorrect because Light waves do not need a medium to pass through it while Sound waves need a medium to pass through it.

B) This is incorrect as explained above.

C) This is incorrect because Light waves do not carry energy parallel to the motion of the wave.

Light waves are transverse waves, as so they carry energy perpendicular to the motion of the wave while Sound waves are longitudinal waves and so, they carry energy parallel to the motion of the wave.

D) This is correct because Sound waves carry energy parallel to the motion of the wave.

Sound waves are transverse waves, as so they carry energy parallel to the motion of the wave while Light waves are longitudinal, as so they carry energy perpendicular to the motion of the wave.

Answer:

D-Sound waves carry energy parallel to the motion of the wave, while light waves carry energy perpendicular to it.

Explanation:

To calculate the distance that it will take to bring the car to a stop, we can use the equations of motion. The force of kinetic friction can be calculated by multiplying the coefficient of friction by the normal force. Using the equations v = u + at and s = ut + 0.5at^2, we can find the distance.

To calculate the distance that it will take to bring the car to a stop, we can use the equations of motion. The force of kinetic friction can be calculated by multiplying the coefficient of friction by the normal force. The normal force is equal to the weight of the car, which is given by the mass of the car multiplied by the acceleration due to gravity. The force of kinetic friction is equal to the mass of the car multiplied by the acceleration. Rearranging the equation F = ma to solve for acceleration gives us a = F/m. Substituting the force of kinetic friction for F and the mass of the car for m, we can find the acceleration. Using the equation v = u + at, where v is the final velocity (0 m/s), u is the initial velocity (20.0 m/s), a is the acceleration, and t is the time, we can solve for t. Finally, we can use the equation s = ut + 0.5at^2 to calculate the distance s that it will take to bring the car to a stop. Plugging in the values for u, t, and a will give us the answer.

Answer:

[tex]\frac{dQ}{dt} =-hA\Delta T(t)[/tex]

Explanation:Newton.s law of cooling states that the rate of cooling of an object is proportional to the difference between its own temperatures and temperature of its surroundings. Mathematically,

[tex]\frac{dQ}{dt} =-hA [T(t)-T(s)]\\[/tex]

[tex]\frac{dQ}{dt} =-hA\Delta T(t)[/tex]

where [tex]Q[/tex] is the heat transfer

[tex]h[/tex] is heat transfer coefficient

[tex]A[/tex] is the heat transfer surface area

[tex]T[/tex] is the temperature of the object's surface

[tex]T(s)[/tex] is the temperature of the surroundings

Final answer:

Newton's Law of Cooling can be expressed using a differential equation: dQ/dt = -k(T - Ts).

Explanation:

Newtons's Law of Cooling states that the rate of cooling of an object is proportional to the difference between its temperature and the temperature of its surroundings. In this particular situation, we can express this law using a differential equation:

dQ/dt = -k(T - Ts)

Where:

Given Information:

Radius = r = 0.31 m

Potential difference = V = 1375 Volts

Required Information:

charge = q = ?

Answer:

q = 4.741x10⁻⁸ C

Solution:

[tex]V = kq/r[/tex]

Where k = 8.99x10⁹ N.m²/C² is the Coulomb's constant

Re-arranging the equation to find the q

[tex]q = Vr/k[/tex]

q = (1375*0.31)/8.99x10⁹

q = 4.741x10⁻⁸ C = 47.41 nC

Answer:

Technician B

Explanation:

The current amp value at the battery position is the current value. The current is the same everywhere for a series circuit without any connecting points. The current at the position of the battery is the same as in each resistor position.

Final answer:

Technician B is correct: current is the same in all parts of a series circuit. Technician A is incorrect: current divides in the branches of a parallel circuit and is not the same. The sum of branch currents equals the total current in parallel circuits.

Explanation:

Understanding Current in Series and Parallel Circuits

Technician B is correct when they say current is the same everywhere in a series circuit. In a series circuit, there is only one path for the current to flow, thus the current (I) is identical through any component in the series, as stated: I = I1 = I2 = I3. This principle is known as the first principle of series circuits. On the other hand, Technician A is incorrect in suggesting current is the same in each branch of a parallel circuit. In parallel circuits, the current divides at each junction and the total supplied current is the sum of the currents in the various branches.

So, in summary, in a series circuit, the current is constant through all components, and the total voltage drop across all components adds up to the voltage supplied by the source. In a parallel circuit, meanwhile, each resistance experiences the same voltage difference, while the current through each branch may vary depending on the resistance of that branch.

Answer:

180m

Explanation:

V = Final velocity = 18

U = Initial Velocity = 12

a = Acceleration = (18-12)/12 = 6/12 = 0.5

d = ?

V² = U² + 2ad

18² = 12² + 2*0.5*d

324 = 144 +d

d = 324 - 144

d = 180m

Final answer:

The boy travels a distance of 180 meters. This calculation is based on the kinematic equations for uniformly accelerated motion using the given initial and final velocities and the time taken.

Explanation:

The subject of the question is Physics, and it appears to be at a High School level. The problem deals with kinematics, specifically the equations of motion for an object with constant acceleration. To find the distance traveled by the boy sledding down the hill, we can use the kinematic equation: s = ut + ½ at², where s is the distance, u is the initial velocity, t is the time, and a is the acceleration. The initial speed u is given as +12 m/s, the final velocity v is +18 m/s, and the time t is 12 seconds. We first find the acceleration using the formula a = (v - u) / t. Substituting the known values, we get a = (18 m/s - 12 m/s) / 12 s = 0.5 m/s². Now we can calculate the distance s using the kinematic equation: s = (12 m/s)(12 s) + ½(0.5 m/s²)(12 s)² = 144 m + 36 m = 180 m. Therefore, the boy travels a distance of 180 meters.

Answer:

h= 161.06 m

Explanation:

Given that

Speed of the sound ,C= 343 m/s

Total time ,t= 6.2 s

lets take the depth of the well = h

The time taken by stone before striking the water = t₁

we know that

[tex]h=\dfrac{1}{2}gt_1^2[/tex]

[tex]t_1=\sqrt{\dfrac{2h}{g}}[/tex]

The time taken by sound =t₂

[tex]t_2=\dfrac{h}{343}[/tex]

The total time

t = t₁+ t₂

[tex]6.2 = \sqrt{\dfrac{2h}{g}}+\dfrac{h}{343}[/tex]

[tex]6.2 = \sqrt{\dfrac{2h}{9.81}}+\dfrac{h}{343}[/tex]

Now by solving the above equation we get

h= 161.06 m

Therefore the depth of the well will be 161.06 m.

A. Hannah should choose copper for her pot because it has the lowest specific heat, and  she should choose wood for her spoon because it has the highest specific heat

Explanation:

The specific heat capacity of a substance is the amount of heat required to increase the temperature of 1 kg of the substance by 1 degree.

Mathematically:

[tex]C=\frac{Q}{m\Delta T}[/tex]

where

Q is the amount of heat supplied to the substance

m is the mass of the subtsance

[tex]\Delta T[/tex] is the increase in temperature

This means that:

In this situation, we want:

Therefore, the most reasonable choice in this situation is:

A. Hannah should choose copper for her pot because it has the lowest specific heat, and  she should choose wood for her spoon because it has the highest specific heat

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Answer:

D, A & B, C, E

Explanation:

In each problem, sum the torques about the edge of the table.

A) ∑τ = Iα

mg (-1.5 m) + (100 kg) g (1.5 m) = 0

m = 100 kg

B) ∑τ = Iα

mg (-0.75 m) + (100 kg) g (0.75 m) = 0

m = 100 kg

C) ∑τ = Iα

mg (-1.5 m) + (100 kg) g (0.75 m) = 0

m = 50 kg

D) ∑τ = Iα

mg (-1.5 m) + (200 kg) g (1.5 m) = 0

m = 200 kg

E) ∑τ = Iα

mg (-1.5 m) + (100 kg) g (0.5 m) = 0

m = 33.3 kg

Answer:

DL = 1.5*10^-4[m]

Explanation:

First we will determine the initial values of the problem, in this way we have:

F = 60000[N]

L = 4 [m]

A = 0.008 [m^2]

DL = distance of the beam compressed along its length [m]

With the following equation we can find DL

[tex]\frac{F}{A} = Y*\frac{DL}{L} \\where:\\Y = young's modulus = 2*10^{11} [Pa]\\DL=\frac{F*L}{Y*A} \\DL=\frac{60000*4}{2*10^{11} *0.008} \\DL= 1.5*10^{-4} [m][/tex]

Note: The question should be related with the distance, not with the diameter, since the diameter can be found very easily using the equation for a circular area.

[tex]A=\frac{\pi}{4} *D^{2} \\D = \sqrt{\frac{A*4}{\pi} } \\D = \sqrt{\frac{0.008*4}{\\pi } \\\\D = 0.1[m][/tex]

Answer:

81 mm from the center

Explanation:

5.67g = 0.00567 kg

33.3 revolutions per minute = 33.3 (rev/min) * 2π (rad/rev) * (1/60) (min/sec) = 3.487 rad/s

The weight of the coin is product of mass and gravitational acceleration g = 9.81m/s2

W = mg = 0.00567 * 9.81 = 0.0556 N

Which is also the normal force of the record acting back on the coin to balance it.

Them the static friction is product of normal force and friction coefficient

[tex]F_f = N\mu = 0.0556*0.1 = 0.00556 N[/tex]

For the coin to NOT slip off, its centripetal force should at most be equal to the static friction

[tex]F_c = 0.00556[/tex]

[tex]a_cm = 0.00556[/tex] Newton's 2nd law

[tex]a_c = 0.00556 / 0.00567 = 0.981 m/s^2[/tex]

The centripetal acceleration is the product of squared angular velocity and radius of circular motion

[tex]a_c = \omega^2r[/tex]

[tex]r = \frac{a_c}{\omega^2} = \frac{0.981}{3.487^2} = 0.081m[/tex] or 81 mm

Answer:

The car that went 54 km in 2/3h was faster, 5/4 times faster than the other car

Explanation:

Average speed of a car is the ratio between the displacement [tex]\Delta x [/tex] and the time (t) it takes to do that displacement:

[tex]V_{avg}=\frac{\Delta x}{t} [/tex]

So, for the first car:

[tex]V_{avg1}=\frac{60km}{\frac{5h}{6}} =72\frac{km}{h} [/tex] (1)

for the second car we have:

[tex]V_{avg2}=\frac{60km}{\frac{2h}{3}} =90\frac{km}{h} [/tex] (2)

So, the second cart is faster than the first one. To find how many times divide speed 2 by speed 1:

[tex]\frac{90}{72}=\frac{5}{4} [/tex]

Explanation:

When a conductor moves in the magnetic field , the emf is generated across its ends . Which can be calculated by the relation

emf  ξ = B x l x v

here B is the magnetic field strength , l is the length of conductor and v is its velocity .

In our question B = 5.4 x 10⁻⁵ T

l = 2.30 x 10⁴ m  and v = 7.5 x 10³

Thus  ξ = 5.4 x 10⁻⁵ x 2.30 x 10⁴ x 7.5 x 10³ = 9.3 x 10³ Volt

Answer:

Explanation:

Given

Weight of rifle [tex]W=25\ N[/tex]

mass of rifle [tex]M=\frac{25}{10}=2.5\ kg[/tex]

mass of bullet [tex]m=4\ gm[/tex]

speed of bullet [tex]u=290\ m/s[/tex]

As there is no net force on the bullet-rifle system therefore momentum is conserved

[tex]0=Mv+mu[/tex]

[tex]v=-\frac{mu}{M}[/tex]

[tex]v=-\frac{4\times 10^{-3}\times 290}{2.5}[/tex]

[tex]v=-0.464\ m/s[/tex]

i.e. opposite to the direction of bullet speed

(b)Weight of Man [tex]=750\ N[/tex]

Combined weight of man and rifle[tex]=750+25=775\ N[/tex]

mass of man-rifle system [tex]M'=\frac{775}{10}=77.5\ kg[/tex]

Now man and rifle combinedly recoil

therefore

[tex]0=(M')v '+mu [/tex]

[tex]v'=-\frac{mu}{M'}[/tex]

[tex]v'=-\frac{4\times 10^{-3}\times 290}{77.5}[/tex]

[tex]v'=0.0149\ m/s[/tex]

Answer:

3.3 m/s

Explanation:

The question is incomplete, here is the complete question:

After skiding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of 2.7 m/s. Miranda runs after her at a velocity of 4.1 m/s and hops on the inner tube. How fast do the two of them slide across the snow together on the inner tube? Ashley's mass is 71 kg and Miranda's is 58 kg. Ignore the mass of the inner tube and any friction between the inner tube and the snow.

SOLUTION:

mass of Ashley (Ma) = 71 kg

mass of Miranda (Mm) = 58 kg

initial velocity of Ashley (Va) = 2.7 m/s

initial velocity of Miranda (Vm) = 4.1 m/s

Find the final velocity (Vf) at which they both slide together

from the conservation of momentum, initial momentum = final momentum

Ma.Va + Mm.Vm = (Ma + Mm) . Vf

[tex]Vf = \frac{Ma.Va + Mm.Vm}{Ma + Mm} \\ Vf=\frac{(71 x 2.7) + (58 x 4.1)}{71+58}[/tex]

Vf = (191.7 +237.8) / (129)

Vf = 3.3 m/s

Answer:

Net force = 129.4, Force as multiple of weight of her hand = 18.84

Explanation:

Given Data:

Total body weight = 56.0 kg   ;

no. of turns = 2.5/second        ;

hand to hand distance = 1.5m ;

weight of hand = 1.25% of body weight ;

Solution:

mass of hand = [tex]\frac{1.25}{100}[/tex]*56 = 0.7kg ;

radius = d/2 = 1.5/2 = 0.75m     ;

Now we need to find velocity, as we know that velocity can be calculated by dividing distance by time

v = d/t = [tex]\frac{2.5*2*3.14*0.75}{1}[/tex] = 11.775 m/s or 12 m/s;

a.

The formula to calculate force is given as

F = mv²/r = (0.7*11.775²)/0.75 = 129.4 N

b.

To calculate force as multiple of weight on her hand, we need to calculate the gravitational force W on her hand first.

W = gm = 9.81 * 0.7 = 6.867 N

Now the wieght on her hand can be represented by

[tex]\frac{Force_{net} }{weight of hand}[/tex]  = 129.4 / 6.867 = 18.84

The force that the ice skater exerts on her hand (150N) is roughly 22 times the weight of her hand (6.86N). She achieves this by spinning with her arms outstretched.

The skater's hand, as given by biometric measurements, makes up about 1.25% of her body weight. Since her body weight is 56.0kg, her hand weight would be 0.0125 * 56.0kg = 0.7kg. In terms of newtons (N), when we consider the acceleration due to gravity as approximately 9.8 m/s², the weight of her hand becomes 0.7kg * 9.8 m/s² = 6.86N. Thus, if we're asked to express the force that her wrist exerts on her hand (150N) as a multiple of the weight of her hand, we'll divide the two forces. Namely, F_hand/F_weight = 150N/6.86N which is approximately 21.86. Therefore, the force her wrist exerts on her hand is roughly 22 times the weight of her hand.

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Answer: TRUE

Explanation:Jump starting a car is a process of starting a car whose battery is Dead,which means it doesn't have enough battery life to start a Car.

The process involves bringing both cars close to each other and Connecting the positive side of a good battery to the positive side of the Dead battery using a JUMPER CABLES,

Connect the positive cable to the positive side of the working battery,

Connect the Negative cable to the Negative side of the working battery,

Finally,connect the Negative cable to a grounded meta part of the car we want to JUMP START.

The phrase "positive to positive, negative to ground" is true when jump starting a car.

The phrase "positive to positive, negative to ground" is true when jump starting a car.

When jump starting a car, it is important to connect the positive terminals of both the donor and recipient vehicles using jumper cables. Then, the negative terminal of the recipient vehicle should be connected to a grounded metal surface, such as the engine block or a bolt on the frame.

By following this phrase, you ensure that the electrical current flows in the correct direction, providing a safe and effective way to start a car with a dead battery.

Learn more about electrical current here:

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Answer:

v₂ = 395.83 m/s

Explanation:

given,

Average speed of nitrogen molecule, v₁ = 475 m/s

Temperature in summer, T₁ = 300 K

Average speed of nitrogen molecule in winter, v₂ = ?

Temperature in winter, T₂ = 250 K

The relation of average speed with temperature

          [tex]v\ \alpha\ \sqrt{T}[/tex]

now,

        [tex]\dfrac{v_2}{v_1} = \dfrac{\sqrt{T_2}}{\sqrt{T_1}}[/tex]

        [tex]\dfrac{v_2}{475} = \dfrac{\sqrt{250}}{\sqrt{300}}[/tex]

                     v₂ = 0.833 x 475

                     v₂ = 395.83 m/s

The average speed on a frigid winter day is equal to v₂ = 395.83 m/s