Question

A stone is projected from the ground with velocity $50m/s$ at an angle ${30}^{\circ }$ with horizontal. It crosses a wall after $3/s$. How far beyond the wall the stone will strike the ground? $(g=10m/s^2)$.

• A. $90.2m$
• B. $12.5m$
• C. $86.5m$
• D. $125\sqrt{3}m$

Answer 1

The correct option is C $86.5m$

$Time,T=\frac{2u\sin \theta }{g}$
$T=\frac{2\times 50\times \sin {30}^{\circ }}{10}$
$=\frac{2\times 50\times \frac{1}{2}}{10}=5s$
Time spent after crossing the wall, $t_2=5-3=2s$
$\therefore Distance,x_2=u\cos \theta \times 1_2$
$=50\times \cos {30}^{\circ }\times 2$
$=50\times \frac{\sqrt{3}}{2}\times 2$
$=50\sqrt{3}$
$=50\times 173$
$=86.5m$.