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Question

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


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Solution

Step 1: Given Data

Initial velocity for upward motion =u

The final velocity for upward motion be v=0.

Initial velocity for the downward motion u=0

The final velocity for downward motion be v.

Let the acceleration due to gravity be g.

Let the time taken be t.

Step 2: Time Taken for Upward Motion

For the vertically upward motion g is negative as it opposes the motion.

According to Newton's first law of motion

v=u-gt

0=u-gt

t=ug 1

Step 3: Time Taken for Downpward Motion

For vertically downward motion g is positive as it is in the direction of motion.

According to Newton's first law of motion

v=u+gt

v=0+gt

t=vg 2

Step 4: Calculate Final velocity

From equation 1 and 2 we get

t=ug=vg

v=u

Hence, the velocity with which the ball falls on the ground is u.


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