Question

A body is projected horizontally from a height of $20m$. It reaches the ground at a horizontal distance of $40m$. The speed of particle when it hits the ground is

• A. $10m/s$
• B. $10\sqrt{2}m/s$
• C. $20m/s$
• D. $20\sqrt{2}m/s$

Answer 1

The correct option is D $20\sqrt{2}m/s$

R = 40 m ; it was projected horizontally

So that horizontal velocity $=\frac{R}{t}$

t = time ti free fall a height 20 m

$\downarrow$

as initial vertical velocity = 0

Given by $h=\frac{1}{2}9t^2$ we have t $=\sqrt{\frac{2h}{9}}$

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

& vertical velocity gained in these 2 sec

$v_y=u+9t=0+10\times 2=20$ m/s

Horizontal velocity $v_x=\frac{R}{t}=\frac{40}{2}=20m/s$ (constant)

$\Rightarrow$ speed $=\sqrt{v_y^2+v_x^2}=20\sqrt{2}$ m/s