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.
That is, 43 v = 200
⇒ v = 200/43 = + 4.65 m s–1
The girl on cart would move with a velocity of 4.65 m s–1 in the direction in which the girl jumped