2019 TWO(d)

The Wynyard Crossing bridge in Auckland can be raised and lowered to allow tall boats to
sail through when open, and pedestrians to walk across when closed. The bridge consists of
two arms, each of length 22 metres.

When the bridge is rising, the angle of the bridge arm above the horizontal increases at the
rate of $0.01\mathrm{rad}{\mathrm{s}}^{-1}$.

Find the rate at which the height, BH, is increasing when H is 15 metres above the horizontal,
FB.

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