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 

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

c. Findand 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?

Transcribed Image Text:

do -10 eve² – 100 de do lim l→10+ dl