Question

With what speed must an object be thrown vertically upwards to reach a height of $91.5m$? (Take $a=9.8m{s}^{-2}$)

Answer 1

Let the initial velocity be '$u$'.
On reaching the maximum height, final velocity $v=0$.
Height, $s=91.5m$ and acceleration, $a=-9.8m{s}^{-2}$
Using the third equation of motion,
$v^2=u^2+2as$,
$0^2=u^2-2\times 9.8\times 91.5$
$\Rightarrow u=42.3m{s}^{-1}$

Therefore the object should be thrown vertically up with a speed of $42.3m{s}^{-1}$.