A particle is projected from a point P with a velocity v at an angle `theta` with horizontal. At a certain point Q it moves at right angles to its initial direction. Then

Options

A. `mv^(2) sin theta`
B. zero
C. `-mv^(2) sin theta`
D. `-(mv^(2) sin theta)/(2)`

Answer

D

Explanation

`W_("net") = K_(f) - K_(i) = (1)/(2) m (v cos theta)^(2) = (1)/(2) mv^(2)`
` (1)/(2) mv^(2) [ cos^(2) theta - 1] = - (1)/(2) mv^(2) sin^(2) theta`