Question

A 9000 kg locomotive moving at 4.0 m/s links up with a stationary boxcar of mass 5000 kg. With what velocity will the combined cars move immediately after the collision?

a. 2.6 m/s
b. 7.2 m/s
c. 2.4 m/s
d. 3.0 m/s

Answer 1

The velocity of the combined cars immediately after the collision, calculated using the conservation of momentum, is approximately 2.6 m/s, which corresponds to option a.

Step-by-step explanation:

The question involves applying the principle of conservation of momentum, which states that if no external forces act on a closed system, the total momentum of the system remains constant. In the scenario provided, a locomotive with a mass of 9000 kg moving at 4.0 m/s links up with a stationary boxcar of mass 5000 kg. To find the velocity of the combined cars immediately after the collision, we use the formula:

m1 * v1 + m2 * v2 = (m1 + m2) * vf

Plugging in the known values:

9000 kg * 4.0 m/s + 5000 kg * 0 m/s = (9000 kg + 5000 kg) * vf

This simplifies to:

36000 kg*m/s = 14000 kg * vf

Dividing both sides by 14000 kg gives us:

vf = 2.57 m/s

Therefore, immediately after the collision, the combined cars will move with a velocity of approximately 2.6 m/s, which corresponds to option a.