Engineering Board Exam Reviewer · Related Rates (Time Rates) · hard
A person walks along a straight path at 4 ft/s. A searchlight on the ground 20 ft from the path rotates to keep its beam on the person. Find the rate at which the beam is rotating when the person is 20 ft from the point on the path nearest the searchlight.
- 0.1 rad/s
- 0.2 rad/s
- 0.05 rad/s
- 0.141 rad/s
Answer
A. 0.1 rad/s
Solution
Let be the beam angle from the perpendicular, x the distance along the path: =x/20. Differentiating: 2 /dt=1/20dx/dt. At x=20, 2 =2. So 2d /dt=4/20=0.2 d /dt=0.1 rad/s.
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