8. An empty toy train car of mass 50 kg coasts along at 5 m/s. A 10-kg toy is suddenly dropped vertically into the car. Find the speed of the car immediately
after the toy is dropped in.
A. 0.5 m/s
B. 4.2 m/s
C. 5 m/s
D. 50 m/s

The correct option is;

B. 4.2 m/s

Explanation:

The mass of the toy train car in motion = 50 kg

The velocity of the toy train car = 5 m/s

The mass of the toy vertically dropped into the car = 10 kg

Therefore, we have from the conservation of linear momentum;

The initial momentum of the train car = The total momentum of the train car and toy

The initial momentum of the train car is given as follows;

Momentum = Mass × Velocity

Initial momentum of the train car = Mass of the train car × Velocity of the train car

Initial momentum of the train car = 50 kg × 5 m/s = 250 kg·m/s

The total momentum of the train car and toy = (Mass of the toy + Mass of the train car) × Final speed immediately after the toy is dropped

The total momentum of the train car and toy = (10 kg + 50 kg) × v = 60 kg × v

Given that the initial momentum of the train car = The total momentum of the train car and toy

We have;

250 kg·m/s =  60 kg × v

v = 250 kg·m/s/(60 kg) = 4.1 m/s

v = 4.1 m/s ≈ 4.2 m/s

∴ The speed immediately after the toy is dropped, v ≈ 4.2 m/s.