Question

A ball is dropped from an elevator at an altitude of 200 m. How much time will the ball take to reach the ground if the elevator is:
a.Stationary?
b.Ascending with velocity 10 $m{s}^{-1}$?
c.Descending with velocity 10 $m{s}^{-1}$?

Answer 1

$\overrightarrow{S}=\overrightarrow{\mu }t+\frac{1}{2}\overrightarrow{a}{t}^2\left(a\right)200=0t+\frac{1}{2}\times 10\times t^2{t}^2=40\Rightarrow t=\left(2\sqrt{10}\right)seconds$

$\left(b\right)200=-10t+\frac{1}{2}10t^{2}40=-2t+t^{2}or,t^2-2t-40=0t=\frac{2\pm \sqrt{4+160}}{2}=\frac{2\pm \sqrt{164}}{2}=(1+\sqrt{42})seconds$

$\left(c\right)200=10t+\frac{1}{2}10t^2\Rightarrow 40=2t+t^2{t}^2+2t-40=0t=\frac{-2\pm \sqrt{4+160}}{2}=(\sqrt{42}-1)seconds$