Question

A projectile is fired horizontally at $100m{s}^{-1}$ from the top of hill $500m$ high a target.Find the time taken by the projectile to reach the ground , the distance of the target from the hill and the velocity with which the projectile hits the ground.

Answer 1

Calculating the time taken by the projectile to reach the ground:

$s=ut+\frac{1}{2}g{t}^2$

$500m=\left(100m/s\right)t+\frac{1}{2}\left(9.8m/s^2\right)t^2$

$500=100t+4.9t^2$

$t=4.15s$

Calculating the distance of the target from the hil:

Range = $ut=\left(100m/s\right)\left(4.15s\right)=415m$

Calculating the velocity with which the projectile hits the ground:

$v=100m/s+\left(9.8m/s^2\right)(4.15s{)}^2=268.78m/s$