Question

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

Answer 1

Answer: 3

Here, $u_x=u,u_y=0,a_y=-g=-10m{s}^{-2},a_x=0$

From figure, $u_x=v_0\cos 53^{\circ }$
and $v_y=-v_0\sin 53^{\circ }$
$\because v_x=u_x+a_{x}t$
$\Rightarrow v_y=u_y+a_{y}t=0-10t$
Or $-v_0\sin 53^{\circ }=-10t$
$\therefore v_0\sin 45^{\circ }=10t$
$\Rightarrow \frac{v_0\cos 53^{\circ }}{v_0\sin 53^{\circ }}=\frac{u}{10t}$
Or $\cot 53^{\circ }=\frac{u}{10t}$
Here, $AB=\frac{1}{2}g{t}^2=5t^2$ and $OB=ut\cot 53^{\circ }$
$\therefore 1.7=AB+OB=5t^2+ut\times \frac{3}{4}$
$\Rightarrow 1.7=5{\left(\frac{4u}{30}\right)}^2+\frac{3}{4}u\times \frac{4u}{30}$
$\therefore u^2=9$
$\therefore u=3ms{}^{-1}$