Question

A ball is projected from the ground with a speed of $20m/s$ at an angle of 45 with horizontal. There is a wall of $25m$ height at a distance of $10m$ from the projection point. The ball will hit the wall at a height of

• A. $5m$
• B. $7.5m$
• C. $10m$
• D. $12.5m$

Answer 1

The correct option is B $7.5m$

Given,

$u=20m/s$

$g=10m/s^2$

From 2nd equation of motion,

along x-axis

$S_x=u_{x}t+\frac{1}{2}{g}_x{t}^2$

$10=ucos{45}^{0}t+0$

$10=20\times \frac{1}{\sqrt{2}}t$

$t=\frac{1}{\sqrt{2}}sec$

along y-axis

$S_y=u_{y}t+\frac{1}{2}{g}_y{t}^2$

$S_y=usin{45}^{0}t+\frac{1}{2}{g}_y{t}^2$

$S_y=20\times sin{45}^0\times \frac{1}{\sqrt{2}}-\frac{1}{2}\times 10\times \frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}$

$S_y=10-2.5=7.5m$

The correct option is B.