Question

a stone is projected vertically up from the top of a tower 73.5m with velocity 24.5 m/s . find the time taken by the stone to reach the foot of the tower?

Answer 1

The stone's altitude at time $t$ is given by

$y=73.5\,\mathrm m+\left(24.5\dfrac{\rm m}{\rm s}\right)t-\dfrac g2t^2$

where $g=9.80\dfrac{\rm m}{\mathrm s^2}$ is the acceleration due to gravity. The stone reaches the ground when $y=0$:

$0=73.5\,\mathrm m+\left(24.5\dfrac{\rm m}{\rm s}\right)t-\dfrac g2t^2\implies t=7.11\,\rm s$