Lighthouses Figures
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Math Lighthouse question?
The beacon on a lighouse 40 m from a straight shoreline rotates twice per minute.
a) How fast is the beam moving along the shoreline at the moment when the light beam and the shoreline are right angles? (Hint: You need to express d_theta / d_t in radians per minute.)
b) In part a, how fast is the beam moving along the shoreline when the beam hits the shoreline 40 m from the point on the shoreline is the closest lighthouse?
Well i know that i can't figure out part b without part A but both questions stump me, I have no idea how to figure out part A and part B has very strange wording.
Thanks a lot all you smart people you! ^^
Let:
A be the lighthouse,
B be the closest point on the shore,
C be the point where the beam hits the shore,
x be the length of BC,
a be the measure of angle CAB.
Then:
(a)
da / dt = 4pi rad/min.
x / 40 = tan(a)
dx / dt = 40 sec^2(a) (da / dt)
= 160pi sec^2(a)
When a = 0, dx/dt = 160 pi
= 502.7 m/min.
(b)
When x = 40m:
dx / dt = 160pi sec^2(40)
= 856.6 m/min.
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