Question

Two projectiles $A$ and $B$ are thrown from the same point with velocities $v$ and $\frac{v}{2}$ respectively. If $B$ is thrown at an angle ${45}^{\circ }$ with horizontal, what is the inclination of $A$ when their ranges are the same?

• A. ${\sin }^{-1}\left(\frac{1}{4}\right)$
• B. $\frac{1}{2}{\sin }^{-1}\left(\frac{1}{4}\right)$
• C. $2{\sin }^{-1}\left(\frac{1}{4}\right)$
• D. $\frac{1}{2}{\sin }^{-1}\left(\frac{1}{8}\right)$

Answer 1

The correct option is B $\frac{1}{2}{\sin }^{-1}\left(\frac{1}{4}\right)$

$R_A=R_B$
$R=\frac{u^2\sin 2\theta }{g}$
$R_A=\frac{u^2\sin 2\theta }{g}$
$R_B=(v/2{)}^2\frac{\sin (2\times {45}^o)}{g}$
$R_A=R_B$
$v^2\frac{\sin 2\theta }{g}=\frac{v^2}{4}\frac{\sin {90}^o}{g}$
$\sin 2\theta =\frac{1}{4}$
$2\theta ={\sin }^{-1}\left(\frac{1}{4}\right)$
$\theta =\frac{1}{2}si{n}^{-1}\left(\frac{1}{4}\right)$