How to Calculate Water Level and Boat Speed in Conical Reservoir Problems?

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Homework Statement

A draining conical reservoir. Water is flowing at the rate of 50 m^3/min from a shalloe concrete conical reservoir (vertex down) of base radius 45m and height of 6m.

a. How fast (centimeters per minute) is the water level falling when the water is 5m deep?

b. How fast is the radius of the water's surface changing then? Answer in centimeters per minute.

2. Hauling in a dinghy. A dinghy is pulled toward a dock by a rope from the bow through a ring to the dock 6ft above the bow. The rope is hauled in at the rate of 2 ft/sec.

a. How fast is the boat approaching the dock when 10ft of rope are out?

b. At what rate is the angle theta changing then (see the figure)?

Homework Equations

1.

a. Not given, but cone volume = 1/3*pi*r²*h

The Attempt at a Solution

1.

a. dv/dt = 50/(pi)(45)²(5) or dv/dt = 50/(pi)(45y/6)²(6)

b. Nothing.

2.

a. Nothing.

b. Nothing.

 

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