A boat is towed toward a dock by a cable attached to a winch that stands 10

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A boat is towed toward a dock by a cable attached to a winch that stands 10 feet above the water level (see figure). Let u be the angle of elevation of the winch and let ℓ be the length of the cable as the boat is towed toward the dock.

a. Show that the rate of change of θ with respect to ℓ is 

do -10 eve² – 100 de

b. Compute dθ/dℓ when ℓ = 50, 20, and 11 ft.

c. Finddo lim l→10+ dl and explain what happens as the last foot of cable is reeled in (note that the boat is at the dock when ℓ = 10).

d. It is evident from the figure that θ increases as the boat is towed to the dock. Why, then, is dθ/dℓ negative?


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Related Book For  book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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