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

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 × 5 m s^–1 + 3 kg × 0 m s^–1

= 200 kg m s^–1

Total momenta after the interaction

= (40 + 3) kg × v m s^–1 = 43 v kg m s^–1

According to the law of conservation of momentum,

The total momentum is conserved during the interaction.

Þ 43 v = 200

⇒ v = 200/43 = + 4.65 m s^–1

The girl on the cart would move with a velocity of 4.65 m s^–1 in the direction of the pistol in which the girl jumped.