A girl of mass 40 kg jumps with a horizontal velocity of 5 in `ms^(-1)` onto a stationary cart with frictionless wheels. The mass of the cart is 3kg. What is her velocity as the carts starts moving ? Assume that there is no external unbalanced force working in the horizontal direction.

Explanation

Let v be the velocity of the girl on the cart as the cart starts moving.
The total momenta of the girl and cart before the interaction
` = 40 kg xx 5ms^(-1) + 3kg xx 0ms^(-1)`
` = 200 kgms^(-1)`
Total momenta after the interaction
` = (40 + 3) kg xx vms^(-1)`
` = 43 v kgms^(-1)`
According to the law of conservation of momentum, the total momentum is conserved during the interaction. That is,
`43v = 200`
`rArr v = (200)/(43) = + 4.65 ms^(-1)`
The girl on cart would move with a velocity of 4.65 m`s^(-1)` in the direction in which the girl jumped (Fig.)