A girl of mass 40 kg jumps with a horizontal velocity of 5 ms–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 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,
p = 40 kg x 5 ms-1 + 3 kg x 0 ms-1
= 200 kg ms-1
The total momenta after the interaction is,
p' = (40 + 3) kg x v ms-1 = 43 v kg m s-1
According to the law of conservation of momentum, the total momentum is conserved during the interaction.
Therefore,
43 v = 200
v = 200/43
= +4.65 ms-1
The girl on cart would move with a velocity of 4.65 ms–1 in the direction in which the girl jumped onto the cart.
