Question

A 50 kg boy runs at a speed of 10 m/s and jumps onto the cart. The cart is initially at rest. If the speed of the cart with the boy on it is 2.5m/s , determine the mass of the cart

Answer 1

use conservation of momentum

m1v1 + m2v2 = (m1 + m2)v3

50 x 10 + 0 = (50+m) x 2.5
500 = 125 + 2.5m
2.5m = 375
m = 150kg

Answer 2

Mass of the cart is 150 kg.

Explanation:

Mass of the boy = 50 kg

Speed of the boy = 10 meter per second

Momentum of the boy = mv

Where m = mass of the boy

v = velocity of the boy

Momentum of the boy = 50 × 10 = 500 kg meter per second

Let the mass of the cart = m

Therefore, mass of the cart with the boy = (m + 50) Kg

Velocity of the cart after the boy jumps on it = 2.5 meter per second.

Momentum of the cart with boy = (m + 50)2.5

Now by conservation of the momentum,

(m + 50)2.5 = 500

m + 50 =
`(500)/(2.5)`

m + 50 = 200

m = 200 - 50

m = 150 kg

Therefore, mass of the cart is 150 kg.