PROBLEM SOLVING

$(25$ points$)$ In the $($not$-$so$-$distant$)$ future, you finally have purchased your first home and decided to put an in$-$ground pool in the backyard. You decide your pool should be able to hold $15,000$ gallons of water.

A$.$ In an attempt to cut cost, you opt to fill the pool yourself using your garden hose, which has a flow rate of $50$L$//$min$.$ How long does it take you to fill your pool?

B$.$ The pool seems to filling a little slower than you'd like. You get clever and decide to

cover up part of the end of the hose to make the water come out faster. Does this idea work? Explain why or why not.

C$.$ After $9$ hours of waiting, you notice the pool is still not full enough to swim. Against your better judgement, you and your friends decide to use an old fire hose and the hydrant outside to fill your pool. If the hydrant has a flow rate of $3800$L$/$min$,$ how much longer does it take to finally fill the pool?

D$.$ In a show of "masculinity", one of your friends $($we$\text{'}$ll call him Kyle$),$ wants you to point the fire hose at him and spray him. If the end of the fire hose has a nozzle that is $5$ cm in diameter, and the pressure at the nozzle is $50$ psi $,$ what force does the water come out of the hose at$?$

E$.$ Kyle doesn't find this very pleasant and decides to jump into the pool onto a raft where he lounges for the rest of the day. The pool floats and the air inside have a total density of $1225$g$/$m$^(3).$ If the pool float is rectangular with dimensions $2$m x $1$m x $0\mathrm{.}1$ m $,$ determine:

What percentage of the pool float is above water before Kyle gets on it

The buoyant force on Kyle after he gets on the float if $7$ cm of the float is now underwater