draw a diagram. Label P the point on the wall closest to the lighthouse. If the beam strikes the wall at a distance x from P, such that the angle of the beam is θ, then
x/100 = tanθ
1/100 dx/dt = sec^2θ dθ/dt
we know that dθ/dt = π/5
Now just plug in your numbers to find dx/dt or dθ/dt as needed.
A)A lighthouse emits a beam of light that rotates (counterclockwise from a birds-eye perspective) at a constant rate with one full rotation every 10 seconds. 100 feet east of the lighthouse is a long wall running north-south. How fast is the light’s reflection traveling along the wall northwards when it crosses the point on the wall closest to the lighthouse?
B) A mechanic alters the lighthouse to make the light rotate in such a way that its reflection travels northward along the wall at a constant rate of 100 feet per second. How fast, in radians per second, is the beam of light rotating when the light’s reflection is 100 feet north of the point on the wall that is closest to the lighthouse?
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