Question

# A ball is thrown vertically upwards with a velocity $\text{'}u\text{'}$. The velocity with which it falls to the earth again is:

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Solution

## Step 1: Given DataInitial 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 MotionFor 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=\frac{u}{g}$ $\left(1\right)$Step 3: Time Taken for Downpward MotionFor 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=\frac{v}{g}$ $\left(2\right)$Step 4: Calculate Final velocityFrom equation $\left(1\right)$ and $\left(2\right)$ we get$t=\frac{u}{g}=\frac{v}{g}$$⇒v=u$Hence, the velocity with which the ball falls on the ground is $u$.

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