Question

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

• A. $90.2m$
• B. $89.6m$
• C. $86.6m$
• D. $70.2m$

Answer 1

The correct option is C $86.6m$

Time of flight ,$T=\frac{2u\sin \theta }{g}$

$=\frac{2\times 50\times \sin {30}^{\circ }}{10}$

$\frac{100\times \left(1/2\right)}{10}=5s$

Range, $R=\frac{u^2\sin 2\theta }{g}$

$=\frac{2500\times \left(\sqrt{3}/2\right)}{10}=216.5m$

$Now we have time t=3s,

$\frac{t}{T}=\frac{X}{R}$

$\frac{3}{5}=\frac{X}{216.5}$

$X=\frac{3}{5}\times 216.5=129.9m$

The distance beyond the wall where the stone will hit $R-X=216.5-129.9=86.6m$