Question

A stone is projected from the ground with velocity $50 \, m \, s^{- 1}$ 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? $\left(g = 10 \, m \, s^{- 2}\right) \, $

• A. $90.2 \, m$
• B. $12.5 \, m$
• C. $86.5 \, m$
• D. $216.25 \, m$

Answer 1

Answer: (C)

Time, $T=\frac{2 u sin \theta }{g}$
$T=\frac{2 \times 50 \times sin 30^{o}}{10}$
$=\frac{2 \times 50 \times \frac{1}{2}}{10}=5 \, s$
Time spent after crossing the wall, $t_{2}=5-3=2 \, s$
$\therefore $ Distance, $x_{2}=ucos \theta \times t_{2}$
$=50\times cos 30^{o}\times 2$
$=50\times \frac{\sqrt{3}}{2}\times 2$
$=50\sqrt{3}$
$=50\times 1.73$
$=86.5 \, m$