LONG HOMEWORK $01$

In the $2003$ film Pirates of the Caribbean: Curse of the Black Pearl, there is a scene in which

Jack and Will steal $($Commandeer$.$ Nautical term.$)$ a ship of the fleet. They disable the Dauntless

$($another more powerful ship$)$ and hop aboard the Interceptor $($a smaller, faster ship$),$ sailing away

into open waters. The Interceptor was a British Royal Navy Brig, which had a top speed of

$8\mathrm{.}2$ knots. The Dauntless, which was much more heavily armed, was a first$-$rate ship of the line

and could manage a top speed of only $5\mathrm{.}7$ knots. The effective range of such a ship of the line was

about $200$ yards $($longer shots were possible, but at that point, you were more or less relying on

luck$).$

You'll need some conversion factors.

$1$ knot $=0\mathrm{.}51\frac{m}{s}$

$1$ yard $=0\mathrm{.}91m$

At the moment the crew aboard the Dauntless realized Jack and Will were stealing the

Interceptor, the interceptor already had a $20$ second head start $($they started at the same

location$).$ If at the end of this $20$ seconds, the crew of the Dauntless had managed to get

the Dauntless up to full speed, how long would it be until the Interceptor was out of range?

Hint: you can set the final position of the Interceptor to be $x_f+200yds.$

A second crew was aboard a small boat that was out in front of the Interceptor as the

Interceptor sailed away. The boat was moving directly northeast $($as in$,45N$ of $E)$ at a

speed of $3\mathrm{.}1$ knots relative to the water. The water current pointed directly east at

$1\mathrm{.}1$ knots $($relative to the ground$).$ Will, who is aboard the Interceptor, runs to the front

of the Interceptor at a speed of $3\mathrm{.}6\frac{m}{s}($directly north$).$ How fast is the small boat moving

relative to Will?

The crewmen aboard the small boat had to jump off to avoid being crushed by the

Interceptor. At this point, one particular crewman finds himself in the water, $600m$

directly north of the shore. This crewman is a fairly strong swimmer, able to swim at

speeds of $2\mathrm{.}1$ knots $($relative to the water$).$ The location he must reach on the shore is

directly south of him, so he'll need to swim at an angle. How long will it take him to reach

this point?

Hint: you'll need to figure out the angle first.