Question

A ball is thrown horizontally from a height of $20m$. It hits the ground with a velocity three times its initial velocity. The initial velocity of ball is

• A. $2m/s$
• B. $3m/s$
• C. $5m/s$
• D. $7m/s$

Answer 1

The correct option is D $7m/s$

Given that,

Initial speed = u

Height = 20 m

This speed will remain constant throughout the journey.

Horizontal component of velocity when it hits the ground is

$v_x=u$

if $v_y$ be the vertical component of velocity when it hits the ground then,

$v_y^2=2gh$

$v_y^2=2\times 9.8\times 20$

$v_y^2=392m^2/s^2$

Now, final speed of object

$=\sqrt{v_x^2+v_y^2}$

$=\sqrt{u+392}$

Now, according to question

$\sqrt{u+392}=3u$

$9u^2=u^2+392$

$8u^2=392$

$u^2=49$

$u=7m/s$

Hence, the final velocity is $7m/s$