Question

The velocity and direction of projection of a shot which passes in horizontal direction just over the top of a wall which is 50 yards away and 75 feet high :

• A. $40,{30}^{o}C$
• B. $40\sqrt{6},{45}^{o}C$
• C. $50,{60}^{o}C$
• D. None of these

Answer 1

The correct option is B $40\sqrt{6},{45}^{o}C$

$BC$ is maximum height
$\therefore \frac{u^2{\sin }^2\alpha }{2g}=75$
Also $AB$ is horizontal range
$\therefore \frac{1}{2}\frac{\left(2u^2\sin \alpha \cos \alpha \right)}{g}=150$
$\Rightarrow \frac{{\sin }^2\alpha }{2\sin \alpha \cos \alpha }=\frac{75}{150}$
or $\tan \alpha =1$
$\therefore u=\sqrt{75\times 2\times 32\times 2}=40\sqrt{6}$