Not sure how to get actual value without any trig functions in the final answer.

Question

Not sure how to get actual value without any trig functions in the final answer.

A lighthouse stands 400 m off a straight shore and the focused beam of its light revolves three times each minute. As shown in the figure, p is the point on shore closest to the lighthouse and Q is a point on the shore 175 m from P. What is the speed of the beam along the shore when it strikes the point Q? Describe how the speed of the beam along the shore varies with the distance between P and Q. Neglect the height of the lighthouse. Find the related rates equation. When the beam strikes the point Q, its speed along the shore is about (Do not round until the final answer. Then round to the nearest integer as needed.)

Explanation / Answer

tan=x/400

x=400tan

differentiate with respect to time

dx/dt =400sec2 d/dt

dx/dt =400(1+ tan2) d/dt

tan=175/400

revolves3times each minute ==> d/dt =(6pi/60)rad/sec =(pi/10)rad/sec

dx/dt =400(1+(175/400)2) (pi/10)

dx/dt =149.7

dx/dt =150m/s

speed =150m/s

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.