Question

A ball of mass $m$ moving with constant horizontal velocity $u$ strikes a stationary wedge of mass $M$ on its inclined surface as shown in the figure. After collision the ball starts moving up the inclined plane. The wedge is placed on frictionless horizontal surface.
a) Calculate the velocity of wedge immediately after collision.
b) calculate the maximum height the ball can ascend on the wedge.

Answer 1

REF.Image.

collision is elastic then ball move with

same velocity u making the angle $\alpha$

with wedge

Now

Let wedge move with v velocity after collision.

So,

(a) $mu=mu\left(sin\right(90-\alpha \left)\right)+mv$

$mu=mucos2\alpha +mv$

$mv=mu(1-cos2\alpha )$

$mv=2musi{n}^2\alpha$

$V=\frac{2musi{n}^2\alpha }{m}$

(b) Velocity of ball in vertical direction $=ucos(90-u)$

$V_1=usin2\alpha$

$H=\frac{V_1^2}{2g}$

$H=\frac{u^{2}si{n}^{2}2\alpha }{2g}$