Question

10.
A boy of mass 60kg running at 3 m/s jumps on to a trolley of
mass 140 kg moving with a velocity of 1.5 m/s in the same
direction. What is their common velocity.​

Answer 1

Answer:

As the boy jumps on the trolley, the contact forces exerted on the trolley by the boy and on the boy by the trolley cancel each other approximately if we don't consider the effects from quantum perburtation and limiting ourself to classical mechanics.

So, this problem can be solved by Conserving the momentum along the direction of motion of the system comprising of both Boy and the trolley.

Now, since External net force on the system considered = 0

Thus,

Momentum can be conserved here.

Initial momentum = 60*3 + 140*1.5

= 180+210 = 390 kg m/s

Now, as after the jump, the trolley and the boy move together they can be considered as a single particle of mass (60+140) kg = 200 kg

Final momentum = 200 (v)

Initial momentum = Final momentum

390 = 200*v

v can be easily calculated from here and it'll be the common velocity of both the boy and the trolley after the boy jumps on the trolley.