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 it to hit the foot of the plane, the height of the plane (in $\text{m}$ is

Answer 1

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