Question

A ball of mass m moving with velocity vo colliding with a vertical stationary wa perpendicularly as shown in the figure. If coefficient of restitution between the wall and ball is 0.5, then magnitude of velocity of the ball just after the collision will be ​

Answer 1

Answer:

The ball of mass m will reflect normally from the wedge.

Let the velocity of the mass m upon reflection be v

1

.

Apply the conservation of momentum along and perpendicular to the inclined plane of the wedge.

For conservation of momentum along the plane.

MV=mv

0

sinθ−mv

1

sinθ...(1)

For the collision perpendicular to the plane, apply coefficient of restitution.

e=

relativevelocitybeforeimpact

relativevelocityafterimpact

=

−v

0

Vsinθ+v

1

Thus,

Vsinθ+v

1

=−ev

0

...(2)

From (1) :

v

1

=

msinθ

mv

0

sinθ−MV

Substituting in (2),

Vsinθ+

msinθ

mv

0

sinθ−MV

=−ev

0

msinθ

V(msin

2

θ−M)+mv

0

sinθ

=−ev

0

V=

(M−msin

2

θ)

v

0

⋅msinθ(1+e)