Question

A body is projected horizontally with a velocity of $10\text{m/s}$ from the top of an inclined plane of angle ${45}^{\circ }.$ If the body hit the foot of the plane, the height of the plane (in $\text{m}$) is

• A. $10\text{m}$
• B. $20\text{m}$
• C. $30\text{m}$
• D. $40\text{m}$

Answer 1

The correct option is B $20\text{m}$

We know that the horizontal distance travelled by a body projected horizontally with a velocity $u$ from height $h$ is

$x=u\sqrt{\frac{2h}{g}}$
Given $x=h$
$\Rightarrow h=u\sqrt{\frac{2h}{g}}$
$\Rightarrow u^2\frac{2h}{g}=h^2\Rightarrow h=\frac{2u^2}{g}=\frac{2\times {10}^2}{10}=20\text{m}$