2020 TWO(d)

A rocket is fired vertically upwards. Its height above the launch point is given by the formula
$h(t)=4.8t^2$, where $h$ is the height in metres, and $t$ is the time in seconds from firing.

An observer at point A is watching the rocket. She is at the same level as the launch point of
the rocket, and 500 m from the launch point.

Find the rate at which the angle of elevation at A of the rocket is increasing when the rocket is
480 m above the launch point.

*You must use calculus and show any derivatives that you need to find when solving this
problem.*