Question

A car weighing 1000 kg collides with a stationary 50 kg trolley, and imparts a velocity of $75m{s}^{-1}$ to it. Find the speed with which the car was moving (Assume that the car comes to a stop after the collision and neglect friction at the time of collision).

• A. $3.25m{s}^{-1}$
• B. $3.5m{s}^{-1}$
• C. $4.25m{s}^{-1}$
• D. $4.75m{s}^{-1}$

Answer 1

The correct option is C $4.25m{s}^{-1}$

Let the initial velocity and final velocity of the car be $U,V$ respectively.
Let the initial velocity and final velocity of the trolley be $u,v$ respectively.

Given: Mass of car, $M=1000kg$, mass of trolley, $m=50kg$, $v=75m{s}^{-1}$
Initial momentum of car $=MV$
Initial momentum of trolley, $mu=0$ (initially at rest)
Final momentum of car, $MU=0$ (comes to rest after collision)
Final momentum of trolley $=mv$

Using the law of conservation of momentum:
Toatal initial momentum of system = Total final momentum of system
$\Rightarrow MV+0=0+mv\Rightarrow MV$ = $mv$
$\Rightarrow V=\frac{mv}{M}=\frac{50\times 75}{1000}=3.75m{s}^{-1}$
Therefore the initial velocity of car, $V=3.75m{s}^{-1}$