A ball is thrown vertically upwards from ground. It goes to a height $20m$ and then returns to the ground. Taking acceleration due to gravity $g$ to be $10m{s}^{-2}$, find total time of journey of ball.

The correct option is B. $4s$

Given:

Height s = 20 m,

Final velocity, v = 0 (at highest point),

Acceleration due to gravity, $g=-10m/s^2$

Using the third equation of motion, $v^2=u^2+2as$, we get

$0^2+u^2=2as$

or $u=\sqrt{2as}$

$u=\sqrt{2\times 10\times 20}=20m/s$

Now using the second equation of the motion,

$s=ut+\frac{1}{2}a{t}^2$

$20=20\times t+\frac{1}{2}\times (-10)\times t^2$

$t^2-4t+4=0$

On solving the above quadratic equation we get, t = 2 s.

This time is taken by the ball to go upwards. Also, it will take the same to return to the ground.

Thus the total time of the journey of the ball is 4 seconds.