Question

A stone is projected from the ground with velocity $50m{s}^{-1}$ and angle of ${30}^{\circ }$. It crosses a wall after $3s$. How far beyond the wall the stone will strike the ground?
Take $g=10m{s}^{-2}$

• A. $80.5m$
• B. $90.6m$
• C. $86.6m$
• D. $75.2m$

Answer 1

The correct option is C $86.6m$

Time of flight
$T=\frac{2\times 50\times \frac{1}{2}}{10}s=5s$
Time taken by the stone to travel the distance beyond the wall $=5-3=2s$
Horizontal distance travelled in last $2$ seconds,
$x=v_x\times t=v\cos {30}^{\circ }\times t=50\times \cos {30}^{\circ }\times 2$
$=100\times \frac{\sqrt{3}}{2}m=50\sqrt{3}m$
$x=86.6m$