[Math4u] Calculus Help

I have just a couple of questions that are weirding me out. I think
I should be able to get them but the unit analysis is confusing me
more. I am just not really able to form the ininial equations and
such.

Question 1.
A lighthouse is 1 mile off shore, due west. You are on the shore 2
miles north of the point opposite the lighthouse. The light rotates;
if you see the flash every 15 seconds, how fast is the beam moving
when it passes you?

I have an answer of 2/2.625 miles/sec but I don't feel its write
since I feel like I need to use the chain rule (section we are
in)....How would I set up an equation to relate Theta and x miles?
when I differentiate I have d(theta)/dt and I would solve for d
(x)/dt.

Question 2.
A trough is triangular in cross section, an isosceles triangle with
sides of 12 inches and a top of 10 inches. The trough is 40 inches
long. How fast is the depth change if you are pumping 1 cubic
foot/min into the trough. I know the answer will depend upon the
height of the liquid at an instantaneous time (t). I think I kind of
have this one but just want to see another thought.

Question 3.
I am really lost here.
A light is attached to a 13 in radius bicycle tire, at a point 8
inches from the center. If Harvey rides the bike at 15 mph, how fast
is the light moving up and down at its fastest.

I know the light is at a point that is horizontal to the road for the
fastest up and down point.

Thanks in advance for assistance.

William

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