Question

A particle (a mud pallet) of mass 'm' strikes a smooth stationary wedge of mass $M$ with a velocity $v_0$, at an angle $\theta$ with horizontal. If the collision is perfectly inelastic, find the velocity of the wedge just after the collision.

• A. $\frac{m{v}_{0}sin\theta }{m+M}$
• B. $\frac{m{v}_{0}tan\theta }{m+M}$
• C. $\frac{m{v}_{0}cos\theta }{m+M}$
• D. $\frac{M{v}_{0}cos\theta }{m+M}$

Answer 1

The correct option is C

$\frac{m{v}_{0}cos\theta }{m+M}$

Let the system $(M+m)$ moves as a single mass with a velocity $v$.

Conserving the momentum of the system in horizontal, we have $m{v}_{0}cos\theta =(M+m)v$

This gives $v=\frac{m{v}_{0}cos\theta }{M+m}$