A-particle-of-mass-m-strikes-on-ground-with-angle-of-incidence-45-If-coefficient-of-restitution-e-1-2-find-the-velocity-after-impact-and-angle-of-reflection-

Question Number 23049 by Tinkutara last updated on 25/Oct/17

A particle of mass m strikes on ground

with angle of incidence 45 ° . If coefficient

of restitution, e = \frac{1}{\sqrt{2}}, find the velocity

after impact and angle of reflection .

Answered by ajfour last updated on 25/Oct/17

p a r a l l e l t o g r o u n d (i f f r i c t i o n b e

z e r o t h e n) w e c o n s e r v e l i n e a r

m o m e n t u m .

l e t i n i t i a l s p e e d b e v_{0}, a n d f i n a l

s p e e d b e v .

m v \sin θ = {m v}_{0} \sin 45 °

\Rightarrow v \sin θ = \frac{v_{0}}{\sqrt{2}} \dots . (i)

v_{s e p a r a t i o n} = e (v_{a p p r o a c h})

\Rightarrow v \cos θ = \frac{1}{\sqrt{2}} \times v_{0} \cos 45 °

\Rightarrow v \cos θ = \frac{v_{0}}{2} \dots (i i)

(i) \div (i i) g i v e s

\tan θ = \sqrt{2} \Rightarrow θ = \tan^{- 1} \sqrt{2}

v^{2} \sin^{2} θ + v^{2} \cos^{2} θ = \frac{v_{0}^{2}}{2} + \frac{v_{0}^{2}}{4}

\Rightarrow v = \frac{v_{0} \sqrt{3}}{2} .

Commented by Tinkutara last updated on 25/Oct/17

Thank you very much Sir!