Question

A stone is projected from the ground with velocity $50m{s}^{-1}$ and angle of ${30}^{\circ }$ with horizontal. It crosses a wall after $3s$. How far the stone will fall beyond the wall? (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 $T=\frac{2u\sin \theta }{g}=\frac{2\times 50\times \frac{1}{2}}{10}=5s$
Time taken by the stone to travel the distance beyond the wall = $5-3=2s$
Horizontal distance travelled in last $2$ second $=x=v_x\times t=v\cos {30}^{\circ }\times t$
$=50\cos {30}^{\circ }\times 2=100\times \frac{\sqrt{3}}{2}m=50\sqrt{3}m=86.6m$