5. When powder or granular solids are piled up, the powder forms a conical pile. The edge of the pile reaches a certain maximum angle with the horizontal, called the angle of repose.
A pile of coal is found to have an angle of repose of 38 degrees.
a) What is the relationship between the pile and its radius?
b) If a conveyor belt pours the coal onto the pile at a rate of 0.3m^3/min, at what rate is the radius increasing when the radius is 1.7m.
6. An aircraft at an altitude of 10000m is flying at a constant speed on a line that will take it directly over an observer on the ground. If the observer notes that the angle of elevation is 60 degrees and is increasing at a rate of 1 degrees per second, find the speed of the plane in: