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

Options

A. `v=u sqrt(e^(2) sin^(2)theta+cos^(2)theta)`
B. `v=u sqrt(e^(2) cos^(2) theta+ sin^(2) theta)`
C. `v=u sqrt(e^(2) cos^(2) theta +tan^(2) theta)`
D. `v=u sqrt(cot^(2) theta+e^(2) cos^(2) theta)`

Answer

B

Explanation

`v = sqrt((v sin alpha)^(2) +(v cos alpha)^(2))`
`v = sqrt((u sin theta)^(2) +(eu cos theta)^(2))`
`v =u sqrt(e^(2) cos^(2) theta + sin^(2) theta)`.