Question

A ball is thrown vertically upwards with a velocity of $49m/s$. Calculate the total time it takes to return to the surface of the earth.

Answer 1

Step 1: Given Data

The initial velocity of the ball $u=49m/s$

The final velocity of the ball $v=0$

Let the acceleration due to gravity be $g=9.8m/s^2$

Let the time taken to go up be $t$.

Step 2: Calculate the Height

According to Newton's first equation of motion

$v=u-gt$

Acceleration is given as negative since the ball moves upwards against gravity.

$0=49-9.8\times t$

$\Rightarrow 49=9.8\times t$

$\Rightarrow t=\frac{49}{9.8}$

$\Rightarrow t=5s$

Therefore the total time to return to the surface of the earth $=2t=2\times 5=10s$

Hence, the total time the ball takes to return to the surface of the earth is $10s$.