Question

A ball is thrown vertically upwards with a velocity u. Calculate the velocity with which it falls to the earth again.

Answer 1

Given:

u = Initial velocity

Ball is thrown up

Ball goes up and attains a maximum height H and then again comes down.

Let

u = Initial Speed

v = Final Speed

t = time

a = acceleration

s = distance

Case – I

Ball is going upward

a = -g

u = u

v = 0

s = H

Since, v² = u² + 2as

0 = u² - 2gH

H = \(\frac{u^2}{2g}\)......................1

Case – II

Ball comes downward

So, u = 0

v = Final Speed

a = g

since, v² = u² + 2as

v² = 0 + 2gH

 H= \(\frac{u^2}{2g}\)...............2

From equations 1 and 2, we see that,

v = u