Question

A man and a cart move towards each other. The man weighs 32 kg and the cart 16 kg. The velocity of the man is 5.4 km/hr and that of the cart is 1.8 km/hr. When the man approaches the cart, he jumps on to it. The velocity of the cart carrying the man will be

Answer 1

We first convert the velocities to SI unit which is in m/s.

5.4 × 5/18 = 1.5 m/s

1.8 × 5/18 = 0.5 m/s

This is a question on momentum.

By law of conservation of momentum :

Initial momentum = final momentum

Momentum = mass × velocity

Initial momentum

32 × 1.5 = 48

16 × 0.5 = 8

Total = 48 + 8 = 56

Final momentum

Let the final velocity be v

Mass = 16 + 32 = 48 kg

Momentum = 48v

Equating the two we have :

48v = 56

v = 56/48

v = 7/6 m/s

Converting to km/h

7/6 × 18/5 = 21/5 = 4.2 km/h

= 4.2 km/h