Question

An elevator is accelerating upward at a rate of $6ft/{sec}^2$ when a bolt from its ceiling falls to the floor of the lift (Distance=$9.5$ feet). The time (in seconds) taken by the falling bolt to hit the floor is (take $g=32ft/{sec}^2$)

Answer 1

The elevator is accelerating upwards at a rate of 6 ft/$se{c}^2$

Therefore, it's not accelerating in (6+32) ft/$se{c}^2$ [acc = (g+ h]

=38 ft/$se{c}^2$

Now,

S = ut + a$t^2$

9.5 = 0 + $\frac{1}{2}\times 38\times t^2$

$t^2$ = $\frac{9.5}{19}$

$t$ = $\sqrt{0.5}$ = $\frac{1}{\sqrt{2}}$