2023 TWO(e)

A police helicopter is flying above a straight horizontal section of motorway chasing a speeding
car.

The helicopter is flying at a constant speed of $72\mathrm{m}{\mathrm{s}}^{-1}$ and at a constant height of $400$ metres
above the ground. The helicopter is attempting to catch up with the car.

When the direct distance from the helicopter to the car is $2500$ metres, the angle of depression, $\theta$,
between the horizontal and the line of sight from the helicopter to the car is increasing at a rate of
$0.002\mathrm{rad}{\mathrm{s}}^{-1}$.

Calculate the speed of the car at this instant.

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