Question 7
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?

Let the velocity with which the ball strikes the ground be 'v' and time it takes be 't'.
Initial velocity of the ball, u = 0
Distance or height of fall, s = 20 m
Downward acceleration, a = 10 $m{s}^{-2}$
As we know from the third equation of motion, $v^2=u^2+2as$
$=0^2+2\times 10\times 20$
$=400$
$\therefore$ Final velocity of the ball, $v=20m{s}^{-1}$
From the first equation of motion, $t=\frac{v-u}{a}$
$=\frac{20-0}{10}$ $=\frac{20}{10}$ $=2s$