$[$T$1][$Easy$,$ Team, Worksheet$]$ A Runaway Sled You and your team are on the top of an icy

slope that has a steep grade $($i$.$e$.,$ angle of ascent$)$ of $24\mathrm{.}0$o

$,$ and need to pull up a heavy sled

loaded with supplies. You fasten a pulley into the ice at the top of the slope through which you

thread a $150\mathrm{.}0-$ft rope $($which is just long enough to reach the sled$)$ and tie it to the sled. The rope

has a strict tension rating of $450\mathrm{.}0$ lbs$,$ and a warning sticker on one end claims that it will break

if this limit is exceeded by just $10\mathrm{.}0$ lbs$.$ Lined up like a tug$-$o$-$war team, you and six others in

your group steadily pull on the rope with a nearly constant force, resulting in a constant rate of

ascent. However, after exactly $45\mathrm{.}0$ s of pulling, the rope suddenly snaps, and the sled and its

crucial supplies plummet down the hill and disappear into a snow bank. You measure the length

of rope pulled through the pulley before it failed to be $85\mathrm{.}0$ ft$.($a$)$ Neglecting friction, how fast

was the sled going when it reached the bottom of the slope? $($b$)$ For the next attempt to pull the

sled up the slope, you get a stronger rope and want to use a motor$-$driven winch $($it was tiring

work by hand$).$ What should be the minimum power rating of the motor $($in horsepower$)$ in order

that the winch pulls the sled at the same rate as your team had been pulling it by hand? $($Note: $1$

horsepower $=745\mathrm{.}7$ watts$).$