Calculas h/w help

Question

A rotating light is located 11 feet from a wall. The light completes one rotation every 2 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 5 degrees from perpendicular to the wall.

______________ feet per second

Answer 1

This is a Related Rate problem.

One rotation every 2 seconds means dθ/dt = 2π rad / (2 sec) = π rad/sec.

We need to calculate ds/dt at θ = 5° degrees where s is the distance light travels on the wall.

From the sketch below we have tan(θ) = s/11 --> d[tan (θ)]/dt = d[s/11]/dt --> sec²(θ) dθ/dt = (1/11)ds/dt -->

ds/dt = 11sec²(θ) dθ/dt = [11][sec²(5º)][π] = 11π [1/cos(5°)]² = 34.82 feet/second

Wall

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