Question

A particle strikes a horizontal frictionless floor with a speed 'u' at an angle ' ' with the vertical and rebounds with a speed 'v' at an angle '' with the vertical. Find the value of 'v' if 'e' is the coefficient of restitutio

Answer 1

Answer:

Correct option is

D

u

sin

2

θ+e

2

cos

2

θ

As the floor is frictionless and there is no horizontal force, therefore, momentum must be conserved in the horizontal direction.

i.e. musinθ=mvsinϕ

or vsinϕ=usinθ ....(1)

And in vertical direction,

ucosθ

vcosϕ

=e

or vcosϕ=eucosθ ....(2)

Squaring and adding (1) and (2),

v

2

(sin

2

ϕ+cos

2

ϕ)=u

2

sin

2

θ+e

2

u

2

cos

2

θ

v=u

sin

2

θ+e

2

cos

2

θ

.