A child, m $=25\mathrm{.}0$ kg$,$ swings from a rope, L $=9\mathrm{.}8$ m$,$ which hangs above water, d $=2\mathrm{.}9$ m$,$ when vertical. The child is h $=7\mathrm{.}3$ m above the water when she begins to swing.

Part $($b$)$

Assume the child lets go at the bottom of the swing. How long does she take to reach the water, t in seconds?

Part $($a$)$

Write an expression for the velocity v of the student at the bottom of the swing.