Discuss the uses for topographic surveys Match the words in the left column to the appropriate blanks in the sentences on the right. Make certain each sentence is complete before submitting your answer? Help Reset Topographic surveys are used whenever elevation data is required in the end product. Some examples include.(1) creating maps for highway construction ; (2) creating maps for construction design surveys (3) creating maps for flood plain delineation ; (4) creating maps for site location of buildings; and so on.

Answer:

93328 kg

Explanation:

[tex]\rho[/tex] = Density of mud = 1900 kg/m³

Volume of the cuboid is given by

[tex]V=2300\times 750\times 1.4\\\Rightarrow V=2415000\ m^3[/tex]

Volume is also given by

[tex]V=Al\\\Rightarrow l=\dfrac{V}{A}\\\Rightarrow l=\dfrac{2415000}{520\times 520}\\\Rightarrow l=8.9312\ m[/tex]

The length of the cuboid is 0.89312 m

For the small volume

[tex]V_a=al\\\Rightarrow V_a=5.5\times 8.9312\\\Rightarrow V_a=49.12\ m^3[/tex]

Mass is given by

[tex]m=\rho V_a\\\Rightarrow m=1900\times 49.12\\\Rightarrow m=93328\ kg[/tex]

The mass of the mud is 93328 kg

Answer:

Option C. 3 m/s

Explanation:

From the question it is stated that we can neglect the force of air resistance,  therefore there is no force acting on the ball horizontally. From Newton's first law of motion an object will remain at rest or in uniform motion unless acted upon by an external force. thus the ball velocity will remain 3m/s.

Answer:

Time takes the player to read the entire CD is 94.9 minutes.

Explanation:

compact disc (CD) contains 783.216 megabytes of digital information.

Each byte consists of exactly 8 bits.

constant rate of 1.1 megabits per second

How many minutes does it take the player to read the entire CD?

1 Megabites = 1000000 bites

783.216 megabytes = 783216000 bites = 783216000 x 8 = 6265728000 bits

1.1 megabits/s = 1100000 bits/s

thus

t =  6265728000 bits/1100000 bits/s

 = 5696 s

 = 94.9 min

Final answer:

The speed of the ram at the instant of contact is 8.413 m/s.

Explanation:

To find the speed of the ram at the instant of contact, we can use the principle of conservation of mechanical energy. The initial potential energy stored in the compressed spring is converted into the kinetic energy of the ram as it hits the staple. Since the mass of the spring is ignored, we can consider the system as consisting of only the ram.

Using the equation for the potential energy of the spring (PE = 0.5kx^2), we can calculate the initial potential energy. The compressed length of the spring is 3.20 x 10^-2 m, so the initial potential energy is 0.5(37107 N/m)(3.20 x 10^-2 m)^2 = 192.128 J.

At the instant of contact, all of the potential energy has been converted into kinetic energy. Therefore, we can equate the initial potential energy to the final kinetic energy of the ram. The kinetic energy is given by KE = 0.5mv^2, where m is the mass of the ram (0.179 kg) and v is the speed of the ram at the instant of contact.

Solving for v, we have: 192.128 J = 0.5(0.179 kg)v^2. Rearranging the equation and solving for v, we find that v = 8.413 m/s. Therefore, the speed of the ram at the instant of contact is 8.413 m/s.

Answer:

[tex]t=25.6446\ s[/tex]

is the time after which Jill will be able to catch the cart.

Explanation:

Given:

Now the component of gravity acting on the cart along the inclined plane:

[tex]g'=g.sin\ \theta[/tex]

[tex]g'=9.8\times sin\ 3^{\circ}[/tex]

[tex]g'=0.5129\ m.s^{-2}[/tex]

Time taken by Jill to reach this speed:

[tex]v=u+a.t[/tex]

where:

t = time taken

u = initial velocity = 0

[tex]51.289=0+2\times t[/tex]

[tex]t=25.6446\ s[/tex] is the time after which Jill will be able to catch the cart.

Answer:

A) [tex] Z = 0.577 C +112.931[/tex]

[tex] Z = 0.577*(100) +112.931=170.631 Z[/tex]

B) [tex] C=\frac{Z-112.931}{0.577}= \frac{100-112.931}{0.577}=-22.41 C[/tex]

C) [tex] K = C +273.15[/tex]

[tex] K = -22.41 +273.15 =250.739 K[/tex]

Explanation:

For this case we want to create a function like this:

[tex] Z = a C + b[/tex]

Where Z represent the degrees for the Z scale C the Celsius grades and  tha valus a and b parameters for the model.

The boiling point of nitrogen is -195,8 °C

The melting point of iron is 1538 °C

We know the following equivalences:

-195.8 °C = 0 °Z

1538 °C = 1000 °Z

Let's say that one point its (1538C, 1000 Z) and other one is (-195.8 C, 0Z)

So then we can calculate the slope for the linear model like this:

[tex] a = \frac{z_2 -z_1}{c_2 -c_1}= \frac{1000 Z- 0Z}{1538C -(-195.8 C)}=\frac{1000 Z}{1733.8 C}=0.577 \frac{Z}{C}[/tex]

And now for the slope we can use one point let's use for example (-195.8C, 0Z), and we have this:

[tex] 0 = 0.577 (-195.8) + b[/tex]

And if we solve for b we got:

[tex] b = 0.577*195.8 =112.931 Z[/tex]

So then our lineal model would be:

[tex] Z = 0.577 C +112.931[/tex]

Part A

The boiling point of water is 100C so we just need to replace in the model and see what we got:

[tex] Z = 0.577*(100) +112.931=170.631 Z[/tex]

Part B

For this case we have Z =100 and we want to solve for C, so we can do this:

[tex] Z-112.931 = 0.577 C[/tex]

[tex] C=\frac{Z-112.931}{0.577}= \frac{100-112.931}{0.577}=-22.41 C[/tex]

Part C

For this case we know that [tex] K = C +273.15[/tex]

And we can use the result from part B to solve for K like this:

[tex] K = -22.41 +273.15 =250.739 K[/tex]

Final answer:

The boiling point of water on the Z scale is 500°Z. To convert 100°Z to the Celsius scale, the equivalent temperature is 10°C. To convert 100°Z to the Kelvin scale, the equivalent temperature is 283.15 K.

Explanation:

The Z scale is a new temperature scale created by the demented scientist. According to the Z scale, the boiling point of nitrogen is 0°Z and the melting point of iron is 1000°Z.

A) To find the boiling point of water on the Z scale, we need to look at the temperature range between the boiling point of nitrogen and the melting point of iron. Since the boiling point of nitrogen is 0°Z and the melting point of iron is 1000°Z, the range between them is 1000-0 = 1000°Z. Therefore, the boiling point of water on the Z scale is 500°Z, which is halfway between 0°Z and 1000°Z.

B) To convert 100°Z to the Celsius scale, we can use the formula: Celsius = (Z - 0) * (100 - 0) / (1000 - 0). Plugging in the values, we get Celsius = (100 - 0) * (100 - 0) / (1000 - 0) = 10000 / 1000 = 10°C.

C) To convert 100°Z to the Kelvin scale, we use the formula: Kelvin = Celsius + 273.15. Plugging in the value, we get Kelvin = 10 + 273.15 = 283.15 K.

Answer:

Explanation:

Check attachment for answer.

The acceleration of the center of the cylinder and the tension force in the tape is mathematically given as

a=2g/3

T=ug/3

Generally, the equation for the Liner motion  is mathematically given as

Mg-T=Ma

Therefore

Mg.R=(0.5MR^2+MR^2)\alpha

[tex]\alpha=2g/3R[/tex]

b)

Where

a=\alpha R

Hence

a=2g/3

c)

For the tension T

ug-T=Ma

T=u(g-a)

T=ug/3

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Answer: The wavelength of a radio station photon from an AM radio station that broadcast at 1000 kilo-hertz is 3000 m.

Explanation:

To calculate the wavelength of light, we use the equation:

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

where,

= wavelength of the light  = ?

c = speed of light = 300000 km/s = [tex]3\times 10^8m/s[/tex]   (1km=1000m)

[tex]\nu[/tex] = frequency of light = 100kHz = 100000Hz or    (1kHz=1000Hz)

[tex]\lambda=\frac{3\times 10^8m/s}{100000s^{-1}}[/tex]

[tex]\lambda=3000m[/tex]

Thus the wavelength of a radio station photon from an AM radio station that broadcast at 1000 kilo-hertz is 3000 m.

Answer:

A. 3.1m/s²

Explanation:

Since the body is sliding down the plane, the frictional force (Ff) being a force of opposition will be acting upwards.

The forces acting on the body in the vertical direction will be the weight (W) and the normal reaction(R) acting in the opposite direction.

Taking the sum of the forces along the plane,

Fm - Ff = mass × acceleration (newton's law)

Since Fm = Wsin(theta)

Ff = nR where n is the coefficient of friction we will have;

Wsin(theta) - nR = ma... (1)

W = mg = 6×10 = 60N

n = 0.40

R = Wcos (theta) {resolving weight to the vertical)

R = 60cos39°

R = 46.6N

Substituting this values into eqn 1 to the get the acceleration,

60sin39° - 0.4(46.6) = 6a

37.8 - 18.64 = 6a

19.16 = 6a

a = 19.16/6

a = 3.19m/s²

The acceleration of the body down the plane will be 3.1m/s²

Answer:

The time taken by the car with a useful power output is 4.03 seconds.

Explanation:

Given that,

Mass of the car, m = 875 kg

Initial speed of the car, u = 0

Final speed of the car, v = 17 m/s  

Power of the car, P = 42 hp = 31332 W

The power output of the car is given by the work done per unit time. It is given by :

[tex]P=\dfrac{W}{t}[/tex]

Initial kinetic energy of the car will be 0 as it is at rest.

Final kinetic energy of the car is :

[tex]K=\dfrac{1}{2}mv^2[/tex]

[tex]K=\dfrac{1}{2}\times 875\times (17)^2[/tex]

K = 126437.5

As per the work energy theorem, the change in kinetic energy of the object is equal to the work done.

So,

[tex]P=\dfrac{W}{t}[/tex]

[tex]t=\dfrac{W}{P}[/tex]

[tex]t=\dfrac{126437.5}{31332}[/tex]

t = 4.03 seconds

So, the time taken by the car with a useful power output is 4.03 seconds. Hence, this is the required solution.

Answer:

axial stress in the diagonal bar =36,000 psi

Explanation:

Assuming we have to find axial stress

Given:

width of steel bar: 1.25 in.

height of the steel bar: 3 in

Length of the diagonal member = 20ft

modulus of elasticity E= 30,000,000 psi

strain in the diagonal member ε = 0.001200 in/in

Therefore, axial stress in the diagonal bar σ = E×ε

=  30,000,000 psi×  0.001200 in/in =36,000 psi

The stress in the bridge truss diagonal tension member is computed to be 36000 psi, and the elongation of the member under this stress is calculated to be approximately 0.384 inches.

The subject of the question is in the field of Engineering, particularly dealing with the stress and strain effects in a steel structural member of a bridge.

The stress in the member can be calculated using stress and strain relationship along with Young's modulus, given by the formula Stress = Strain x Young's Modulus. Given that strain is 0.001200 in./in. and Young's Modulus (E) is 30,000,000 psi, stress (σ) in the member is σ = E x Strain = 30,000,000 psi x 0.001200 in./in. = 36000 psi.

The steel bar's cross-sectional area can also be calculated as Area = Width x Depth = 1.25 in. x 3 in. = 3.75 in^2. The change in length (∆L) of the member under this stress can be calculated using the formula ∆L = (Stress x Original length) / (Young's Modulus x Area) = (36000 psi x 20 ft) / (30,000,000 psi x 3.75 in^2) = 0.032 ft or 0.384 in.

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Answer:

total magnification = 400 X

Explanation:

given data

ocular lens = 10 X

objective lens = 40 X

to find out

total magnification

solution

we know that total magnification is express as

total magnification = Objective magnification ×  ocular magnification  .................1

put here value we get

total magnification =  10 × 40

total magnification = 400 X

The total magnification for a microscope with a 10X ocular lens and a 40X objective lens is 400X.

When using a microscope, the total magnification can be found by multiplying the magnification of the ocular lens (also known as the eyepiece) by the magnification of the objective lens. Thus, in your case, the total magnification of the specimen being viewed with a 10X ocular lens and a 40X objective lens would be 400X. This is because 10 times 40 equals 400. Therefore, you are observing the specimen at 400 times its actual size.

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Answer:

0.02896 kg/s

Explanation:

[tex]A_1[/tex] = Initial displacement = 0.5 m

[tex]A21[/tex] = Final displacement = 0.1 m

t = Time taken = 0.5 s

m = Mass of object = 45 g

Displacement is given by

[tex]x=Ae^{-\dfrac{b}{2m}t}cos(\omega t+\phi)[/tex]

At maximum displacement

[tex]cos(\omega t+\phi)=1[/tex]

[tex]\\\Rightarrow A_2=A_1e^{-\dfrac{b}{2m}t}\\\Rightarrow \dfrac{A_1}{A_2}=e^{\dfrac{b}{2m}t}\\\Rightarrow ln\dfrac{A_1}{A_2}=\dfrac{b}{2m}t\\\Rightarrow b=\dfrac{2m}{t}\times ln\dfrac{A_1}{A_2}\\\Rightarrow b=\dfrac{2\times 0.045}{5}\times ln\dfrac{0.5}{0.1}\\\Rightarrow b=0.02896\ kg/s[/tex]

The magnitude of the damping coefficient is 0.02896 kg/s

Final answer:

To find the damping constant b for a damped harmonic motion scenario with a given change in amplitude over time, you employ the decay of amplitude formula in damped harmonic motion, then rearrange and solve for b.

Explanation:

To calculate the magnitude of the damping constant b for a 45.0 g hard-boiled egg moving at the end of a spring with a force constant of 25.0 N/m given a decrease in amplitude from 0.500 m to 0.100 m over 5.00 seconds, we apply the principle of damped harmonic motion. The damping force is given by Fx= −bvx, where b is the damping coefficient we wish to find. From the information provided, it's understood that this is a case of exponentially decaying amplitude in harmonic motion.

The equation that relates the exponential decay of amplitude in damped harmonic motion is A(t) = A0e−(bt/2m), where A0 is the initial amplitude, A(t) is the amplitude at time t, and m is the mass of the object. By re-arranging this equation to solve for b, and substituting the given values A0=0.500 m, A(t)=0.100 m, t=5.00 s, and m=0.045 kg (since 45.0 g=0.045 kg), we can calculate b.

The rearranged equation for b would be b = 2m[ln(A0/A(t))]/t. Substituting the values gives b = 2(0.045)[ln(0.500/0.100)]/5.00, which after calculation yields the magnitude of b.

When the altimeter is set to 29.92 inHg, it will read 4,000 feet MSL at a field elevation of 2,000 feet MSL.

To determine the altimeter reading when the field elevation is 2,000 feet MSL (Mean Sea Level) and the altimeter is set to 29.92 inches of mercury (inHg), we need to consider the difference in pressure settings.

The altimeter measures altitude based on the atmospheric pressure. When the altimeter setting (also known as the barometric pressure setting) is changed, it adjusts the reference point for sea level pressure. The standard atmospheric pressure at sea level is approximately 29.92 inHg.

Given:

Field elevation = 2,000 feet MSL

Altimeter setting = 29.92 inHg

We need to find the altimeter reading when the altimeter is set to 29.92 inHg.

To calculate the altimeter reading, we need to determine the difference in pressure between the current pressure (altimeter setting) and the pressure at the field elevation (2,000 feet above sea level).

The standard atmospheric pressure decreases as we go higher in altitude. A typical lapse rate for pressure is around 1 inHg per 1,000 feet of altitude gain. Since the field elevation is 2,000 feet above sea level, the difference in pressure would be approximately 2 inHg.

Therefore, the corrected altimeter reading would be 2,000 feet + 2,000 feet (for the 2 inHg difference) = 4,000 feet MSL.

Hence, when the altimeter is set to 29.92 inHg, it will read 4,000 feet MSL at a field elevation of 2,000 feet MSL.

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Answer:

Force acting on the driver will be 776 N

Explanation:

We have given mass of the driver m = 97 kg

It starts from rest so initial velocity u = 0 m /sec

And reaches to a velocity of 40 m /sec in 5 sec

So final velocity v = 40 m /sec

And time taken t = 5 sec

From first equation of motion v = u +at

So [tex]40=0+a\times 5[/tex]

[tex]a=8m/sec^2[/tex]

Now we have to find the force acting the driver

From newtons law we know that F = ma

So force F = 97×8 = 776 N

So force acting on the driver will be 776 N

Answer:

If the truck were lifted twice as high, it would have twice as much potential energy

Explanation:

Potential energy = mgh

where;

m is mass of the truck (kg)

g is acceleration due to gravity (m/s²)

h is the height above the floor.

Initial Potential Energy, E₁ = mgh₁

When the truck was lifted twice as high, New height (h₂) = 2h₁

New potential Energy, E₂ =mgh₂ = mg(2h₁)

E₂ = 2mgh₁

Recall, E₁ = mgh₁, then substitute in E₁  into E₂

E₂ = 2(mgh₁)

E₂ = 2E₁

Therefore, If the truck were lifted twice as high, it would have twice as much potential energy

Answer:

zero

Explanation:

Work done = - 400 J

In an isothermal process, the temperature remains constant. So, according to the first law of thermodynamics

dQ = dU + dW

As the temperature remains constant and the change in internal energy is the function of change in temperature, here change is temperature is zero so the change in internal energy is also zero.

Final answer:

The change in internal energy of an ideal gas during an isothermal process is 0 J. This is because in an isothermal process for an ideal gas, any work done by the gas is invariably compensated by an equivalent amount of heat absorbed, resulting in no net change in internal energy.

Explanation:

The question pertains to the change in internal energy of an ideal gas during an isothermal process in the context of thermodynamics, specifically according to the first law of thermodynamics. The first law states that the change in internal energy of a system (Triangle U) is equal to the heat added to the system (Q) minus the work done by the system (W). In an isothermal process, the temperature remains constant, and if the process is performed on an ideal gas, the internal energy also remains constant since it depends only on temperature for an ideal gas. Therefore, the change in internal energy ( triangle U) is zero.

In this specific scenario where the work done on the system is -400 J (-W), which means that the system has done 400 J of work on the surroundings. Since no heat transfer information is given, we can infer that in an isothermal process, whatever work is done by the gas is compensated by the heat received from the surroundings, keeping the internal energy unchanged. Thus, the change in internal energy of the gas is 0 J, as the energy spent as work would have been absorbed as heat from the surroundings.

Answer:

The correct options are b. This scale rates an earth quake according to how much damage it causes. and d. This scale uses roman numerals to rank the damage caused by an earth quake.

Explanation:

According to the definition of the Mercalli scale " it is a scale used for the measurement of the intensity of the earthquakes" and was first invented in 1884 by the Italian volcanologist Giuseppe Mercalli. This scale ranges from I to XII.

Answer:

b d

Explanation:

did the quiz

The question involves the application of Newton's law to a ball's position over time, launched from a cannon at an angle. The x and y-axis positions can be calculated using horizontal and vertical principles of motion respectively. For the ball's distance (r) to increase throughout the flight, the launch angle needs to be 90°.

The subject of this question relates to the application of Newton's second law in two dimensions, specifically in cases of projectile motion. The position of the ball fired from a cannon is determined by the initial velocity of the ball, the launch angle θ, and the acceleration due to gravity.

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Answer:

The frequency is 302.05 Hz.

Explanation:

Given that,

Speed = 18.0 m/s

Suppose a train is traveling at 30.0 m/s relative to the ground in still air. The frequency of the note emitted by the train whistle is 262 Hz .

We need to calculate the frequency

Using formula of frequency

[tex]f'=f(\dfrac{v+v_{p}}{v-v_{s}})[/tex]

Where, f = frequency

v = speed of sound

[tex]v_{p}[/tex] = speed of passenger

[tex]v_{s}[/tex] = speed of source

Put the value into the formula

[tex]f'=262\times(\dfrac{344+18}{344-30})[/tex]

[tex]f'=302.05\ Hz[/tex]

Hence, The frequency is 302.05 Hz.

Answer:

The standard free energy is the difference between that of products and reactants. The value of G has a greater influence on the reaction been considered.

Explanation:

The Gibb's free energy also referred to as the gibb's function represented with letter G. it is the amount of useful work obtained from a system at constant temperature and pressure. The standard gibb's free energy on the other hand is a state function represented as Delta-G, as it depends on the initial and final states of the system. The spontaneity of a reaction is explained by the standard gibb's free energy.

Use this hints for any reaction involving the Gibb's free, Enthalpy and entropy.

For each factor of 10 change in Keq, there is a corresponding change of approximately 5.7 kJ/mol in standard free energy change, ΔG°', at standard biochemical conditions (298.15 K).

For every factor of 10 difference in the equilibrium constant, Keq, there is a corresponding change in the standard free energy change, ΔG°', as calculated using the relationship between ΔG°' and Keq:

ΔG°' = -RT ln Keq, where R is the universal gas constant and T is the temperature in Kelvin.

Given that R = 8.314 J/mol·K and at standard biochemical conditions T = 298.15 K, a tenfold change in Keq results in a change of (8.314 J/mol·K x 298.15 K x ln(10)), which equates to approximately 5.7 kJ/mol. Therefore, for example, increasing Keq from 102 to 103 would decrease ΔG°' by 5.7 kJ/mol, making the reaction more product-favored under standard conditions. Conversely, decreasing Keq from 10-3 to 10-4 would increase ΔG°' by 5.7 kJ/mol, making the reaction less product-favored under standard conditions.

Answer:

The ability of water molecules to form hydrogen bonds with other water molecules and water's ability to dissolve substances that have charges or partial charges are due to water's partial charges.

Explanation:

The partial negative charge on oxygen and partial positive charge on hydrogen enables them to make hydrogen bond and also makes it to dissolve the the other substances having partial charges.

Answer:

[tex]v_{avg}=29.499\ m.s^{-1}[/tex]

Explanation:

Given:

distance as a function of time is:

[tex]s=e^t+2-sin\ t[/tex]

Average velocity of the particle from time t=1s to t=5s can be given by the total distance covered divided by the total time consumed.

Position at t=1s:

[tex]s_1=e^1+2-sin\ 1[/tex]

[tex]s_1=3.8768\ m[/tex]

Position at t=5s:

[tex]s_5=e^5+2-sin\ 5[/tex]

[tex]s_5=151.3721\ m[/tex]

Therefore the distance covered during this time is:

[tex]\Delta s=s_5-s_1[/tex]

[tex]\Delta s=151.3721-3.8768[/tex]

[tex]\Delta s =147.4952\ m[/tex]

Now the average speed for the duration:

[tex]v_{avg}=\frac{\Delta s}{\Delta t}[/tex]

[tex]v_{avg}=\frac{147.4952}{5}[/tex]

[tex]v_{avg}=29.499\ m.s^{-1}[/tex]

The rate of seafloor spreading in this area, based on the given radiometric dating results and calculated assuming a constant rate, is 25 km/million years.

To calculate the rate of seafloor spreading, we divide the distance that the seafloor has spread by the amount of time it took. Given the radiometric dating results, we know that this distance (225 km) was covered in 9 million years.

So, the calculation would be: 225 km / 9 million years = 0.025 km/year. Or, to convert this figure to kilometers per million years, you'd multiply by 1 million, giving you a seafloor spreading rate of 25 km/million years.

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Answer:

the magnet or electric current produces a magnetic field

Explanation:

this magnetic field can be visualized as a pattern of a circular field lines surrounding a wire. hall probes can determine the magnitude of the field

hope it helps you

The direction of a magnetic field produced by an electric current in a straight wire can be determined using the right-hand rule. The Biot-Savart law is used to calculate the magnetic field strength at a distance from the wire.

To describe and determine the direction of the magnetic field produced by an electric current, one commonly uses the right-hand rule. For a straight, current-carrying wire, point your right-hand thumb in the direction of the current; then, the direction in which your fingers curl around the wire represents the direction of the magnetic field lines, which form concentric circles around the wire.

For example, if the current flows from right to left in a wire, and you are looking at the wire end-on from the left end, your thumb would point to the left, indicating the direction of the current. Your fingers would naturally curl in a counterclockwise direction, suggesting the magnetic field direction at that point.

For calculating the magnetic field strength, B, produced by a long straight wire carrying current I, the Biot-Savart law can be used. It states that the strength of the magnetic field is directly proportional to the magnitude of the current and inversely proportional to the distance from the wire (assuming the wire is very long compared to the distance).

Answer: The final speed of the balls will be 8.12m/s

Explanation:

For least collision of bodies, both momentum and kinetic energy is conserved.

According to Law of conservation of energy,

The sum of momentum of the objects before collision is equal to the sum of their momentum after collision. Note that the objects will move with a common velocity after impact.

Let m1 and m2 be the masses of the objects

u1 and u2 be their velocities before impact

v be their common velocity after impact

Since momentum is mass × velocity

Mathematically,

m1u1 + m2u2 = (m1+m2)v

Given m1= 3.4kg m2 = 5.7kg u1 = 10.5m/s u2 = 6.7m/s v = ?

Substituting this values in the formula, we have

3.4(10.5)+5.7(6.7) = (3.4+5.7)v

35.7+38.19 = 9.1v

73.89 = 9.1v

V = 73.89/9.1

V= 8.12m/s

Answer:

F=G[tex]\frac{M1XM2}{R^{2} }[/tex]

Explanation:

F=F=G[tex]\frac{M1XM2}{R^{2} }[/tex]

Newton law define gravity as the product of two mass and the mean squired distance between the two bodies.

Where F is the gravitational pull and G is the gravitational constant and M1 and M2 are masses of two bodies while R is their mean distance

Replacing the value in the equation it becomes:

3.2x10N=G[tex]\frac{M1X55}{2.1X10^{2} }[/tex] Where G is the gravitation constant,[tex]6.67x10^{-11}[/tex]

M1=[tex]\frac{3.2X10X(2.1X10)^{2} }{55}[/tex]

M1=[tex]3.8468x10^{-11}[/tex]Kg

Explanation:

Diameter of Sun = 100 x Diameter of Earth.

We are creating a model where Earth is same as golf ball,

Diameter of Earth in model = Diameter of golf ball

Diameter of Earth in model = 1.68 inches

Diameter of Sun in model =  100 x Diameter of Earth in model

Diameter of Sun in model =  100 x 1.68

Diameter of Sun in model =  168 inches = 14 feet

Diameter of Sun in model = 168 inches = 14 feet = 4.27 m

Answer:

35.7 kg

Explanation:

We are given that

Left scale reads =200N

Right scale reads=150 N

We have to find the mass in kg.

We know that

Weight  of child= Sum of two scales=200+150=350 N

Acceleration due to gravity=[tex]9.8 m/s^2[/tex]

We know that

Weight= mg

Using the formula

[tex]350=9.8 m[/tex]

[tex]m=\frac{350}{9.8}=35.7 kg[/tex]

Hence, the mass of child=35.7 kg

Answer:

c. 8.67 cm/s

Explanation:

From the law of conservation of momentum,

Total momentum before the thread was burned = Total momentum after was burned

mu + m'u' = mv + m'v'...................... Equation

Where m = mass of the heavier cart, m' = mass of the lighter cart, u = initial velocity of the bigger cart, u' = initial velocity of the smaller cart, v = final velocity of the bigger cart, v' = final velocity of the smaller cart.

Note: Both cart where momentarily at rest, as  such u = u' = 0. i.e the total momentum before the thread was burn = 0

And assuming the left is positive,

We can rewrite equation 1 as

mv + m'v' = 0............................................ Equation 2

Given: m = 4.5 kg, m' = 1.5 kg, v' = 26 cm/s

Substitute into equation 2,

4.5v + 1.5(26) = 0

4.5v + 39 = 0

4.5v = -39

v = -39/4.5

v = -8.67 cm/s.

Note: v is negative because it moves to right.

Hence the velocity of the 4.5 kg cart = 8.67 cm/s.

The right option is c. 8.67 cm/s

The velocity of the 4.5 kg cart after the thread is burned is 10 cm/s.

When the thread is burned, the compressed spring pushes the carts apart. Since the 1.5 kg cart moves to the left with a speed of 26 cm/s, the 4.5 kg cart would also move to the left but with a slower speed. To determine the velocity of the 4.5 kg cart, we can use the principle of conservation of momentum:

Momentum before = Momentum after

(Mass of 1.5 kg cart) x (Initial velocity) + (Mass of 4.5 kg cart) x (Initial velocity) = (Mass of 1.5 kg cart + Mass of 4.5 kg cart) x (Final velocity)

Solving for the final velocity of the 4.5 kg cart:

(1.5 kg x 26 cm/s + 4.5 kg x 0 cm/s) / (1.5 kg + 4.5 kg) = (6.9 kg) x (Final velocity)

Final velocity = 10 cm/s

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