Question

A particle is projected with speed $u$ at angle $\theta$ with vertical. Find range.

• A. $R=\frac{u^2\sin 2\theta }{2g}$
• B. $R=\frac{u^2\cos 2\theta }{2g}$
• C. $R=\frac{u^2\sin 2\theta }{g}$
• D. $R=\frac{u^2\cos 2\theta }{g}$

Answer 1

The correct option is C $R=\frac{u^2\sin 2\theta }{g}$

Time of flight , $T=\frac{2ucos\theta }{g}$

$\therefore$ Horizontal range, $R=u_{x}T=\left(usin\theta \right)\times \frac{2ucos\theta }{g}=\frac{u^2\left(2sin\theta cos\theta \right)}{g}=\frac{u^{2}sin\left(2\theta \right)}{g}$