Question

A stone is to be projected horizontally from top of a $1.7\, m$ high pole. Calculate initial velocity of projection (in $ms ^{-1}$ ), if it strikes perpendicularly an inclined plane as shown in the figure.

Answer 1

Here, $u_{x}=u, u_{y}=0, a_{y}=-g=-10 \,ms ^{-2}, a_{x}=0$

From figure, $u_{x}=v_{0} \cos 53^{\circ}$
and $v_{y}=-v_{0} \sin 53^{\circ}$
$\because v_{x}=u_{x}+a_{x} t$
$\Rightarrow v_{y}=u_{y}+a_{y} t=0-10 t$
Or $-v_{0} \sin 53^{\circ}=-10 t$
$\therefore v_{0} \sin 45^{\circ}=10 t$
$\Rightarrow \frac{v_{0} \cos 53^{\circ}}{v_{0} \sin 53^{\circ}}=\frac{u}{10 t}$
Or $ \cot 53^{\circ}=\frac{u}{10 t}$
Here, $A B=\frac{1}{2} g t^{2}=5 t^{2}$ and $O B=u t \cot 53^{\circ}$
$\therefore 1.7=A B+O B=5 t^{2}+u t \times \frac{3}{4}$
$\Rightarrow 1.7=5\left(\frac{4 u}{30}\right)^{2}+\frac{3}{4} u \times \frac{4 u}{30}$
$\therefore u^{2}=9$
$\therefore u=3 \,ms { }^{-1}$