Momentum is the ability of imparting or tending to motion to other bodies. The total momentum of a system remains conserved if no external force is acting it. This is calculated by the formula, `vecp=mvecv`. Consider a situation where a cart carrying five boys is moving without friction due to inertia along a straight horizontal road, with a speed of `10m//s`. After travelling certain distance, a boy jumps from the cart with a speed of `2m//s with respect to the cart in opposite direction to it. Then, second boy jumps with the same speed w.r.t. the cart, but in a perpendicular direction to the cart. The mass of the cart is 100 kg and mass of each boy is 20 kg.
The velocity of the cart, just after the second boy has jumped out of it, is

Options

A. `10.202m//s`
B. `10.102m//s`
C. `10.302m//s`
D. `10.402m//s`

Answer

A

Explanation

Using conservation of linear momentum
`160v'+20v'=180vrArrv'=v=10.2`
`160v''+20{-(2-v'')}=0rArrv''~~0.2`
`thereforev_(n et)=sqrt(v'^(2)+v''^(2))=10.202`