# A ball is thrown upward with velocity ‘u’. What will be its velocity when it returns to earth? Explain.

When the ball is thrown vertically upwards with velocity $u,$ at maximum height $h,$ its velocity will be zero $v=0$. $v^2 = u^2 – 2gh$ $0 = u^2 – 2gh$ $\therefore u = \sqrt{2gh}$

The ball comes down to the earth with initial velocity zero $u’=0$ and final velocity $v’$. $v’^2=u’^2+2gh$ $v’^2 = 0 + 2gh$ $\therefore v’ = \sqrt{2gh}$

Thus, we get, $u = v’ = \sqrt{2gh}$

Hence, the ball comes down to the earth with the velocity with which it was thrown vertically upwards.

[Equations used above are deduced from Motion Under Gravity]

Alternative Method

When the ball is thrown vertically upwards with velocity $u$, it reaches the maximum height; its velocity will be zero and the ball returns to the earth. When it reaches the earth, the vertical displacement is zero, which means $h=0$. If $v$ be the velocity with which the ball reaches down to the earth, then

$v^2=u^2-2gh$ $v^2=u^2-2g(0)$ $v^2=u^2$ $\therefore v = u$

Hence, the ball comes down to the earth with the velocity with which it was thrown vertically upwards.

[Equations used above are deduced from Motion Under Gravity]

#### SIMILAR QUESTIONS

A body reaches a certain height when thrown with a certain velocity. What is the height reached if the velocity is doubled?

A body is thrown vertically upwards with a velocity ‘u’. What is the velocity at half the greatest height it can reach?

A body is dropped from a certain point and it travels a height ‘h’ after some time. What would be the height travelled during twice that time?

A body travels from certain location to other with velocity $v_1$ and returns back with uniform velocity $v_2$. Find the average speed.

If the displacement of a body is proportional to square of time, state whether the body is moving with uniform velocity or uniform acceleration.

Can an object have an eastward velocity while experiencing a westward acceleration?