Question

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

• A. $90.2\text{m}$
• B. $89.6\text{m}$
• C. $86.6\text{m}$
• D. $70.2\text{m}$

Answer 1

The correct option is C $86.6\text{m}$

Total time of flight $=\frac{2u\sin \theta }{g}=\frac{2\times 50\times 1}{2\times 10}=5\text{s}$
Time to cross the wall $=3\text{s}$ (given)
Time in air after crossing the wall $=(5-3)=2\text{s}$
$\therefore$ Distance travelled beyond the wall $=\left(u\cos \theta \right)t=50\times \frac{\sqrt{3}}{2}\times 2=86.6\text{m}$
(As horizontal component of velocity will be constant for ground to ground projectile)