Question

A ball is dropped on an inclined plane, its
strikes the plane elastically. After each
collision it's range is R1, R2 and R3
respectively. If R2 =
a(R1 + R3)/6.5, find a.
​

Answer 1

Explanation:

The ball has a velocity v in downward direction just before collision.

Its velocity component parallel to the inclined plane remains constant whereas that of perpendicular to the plane changes from vcosθ to v

′

after the collision.

−vcosθ−0

v

′

−0

=−e ⟹v

′

=evcosθ

As the ball moves in horizontal direction after the collision, thus it makes angle θ with inclined plane

∴ tanθ=

vsinθ

v

′

tanθ=

vsinθ

evcosθ

⟹e=tan

2

θ