These two problems are giving me so much trouble 1. A 24 ton freight car rolls a

Question

These two problems are giving me so much trouble

1. A 24 ton freight car rolls along a straight track with a speed of 10 mi/h. A 2.0 ton automobile falls vertically and lands on it from above and then falls off after a few moments. What is the final speed of the railroad car?

2. A rocket initial mass of 8.0 x 103 kg is fired in the vertical direction. Its exhaust gases are ejected at the rate of 45 kg/s with a relative velocity of 2.4 x 103 m/s. (a) What is the initial acceleration of the rocket? (b) what is the acceleration after 25 s have elapsed?

I attempted 2 parts a and b and both parts were wrong.

a) 13.5 m/s

b) .012 m/s

Can you please help me by showing all steps please!!!

Explanation / Answer

1)

let the final speed of the cars is v m/s

initial mass , m = 24 ton

final mass , M = 24 + 2 = 26 ton

Using conservation of momentum

m * u = M * V

26 * v = 24 * 10

v = 9.23 mi/hr

the final speed of the car is 9.23 mi/hr

2)

let the initial acceleration is a

m * a = dm/dt * v

8 *10^3 * a = 2400 * 45

a = 13.5 m/s^2

the initial accelertion is 13.5 m/s^2

b)

after 25 s

mass . m = 8 *10^3 - 45 * 25 = 6875 Kg

Using second law of motion

6875 * a = 2400 * 45

a = 15.7 m/s^2

the acceleration is 15.7 m/s^2

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