Question

A ball is gently dropped from a height of $20$ $m$. If its velocity increases uniformly at the rate of $10$ $m s^{-2}$, with what velocity will it strike the ground? After what time will it strike the ground?

Answer 1

Let us assume, the final velocity with which ball will strike the ground be $'v'$ and time it takes to strike the ground be $'t'$
Initial Velocity of ball, $u$ =$0$
Distance or height of fall, $s$ = $20$ $m$
Downward acceleration, $a$ =$10$ $m s^{-2}$
As we know, $2as =v^2-u^2$
$v^2 = 2as+ u^2$
= $2 \times 10 \times 20 + 0$
= $400$
$\therefore$ Final velocity of ball, $v$ = $20\; ms^{-1}$
$t = (v-u)/a$
∴Time taken by the ball to strike = $\frac{(20-0)}{10}$

= $\frac{20}{10}$

= $2$ seconds