Thread: Needs some help with some calculus word problems

1. Needs some help with some calculus word problems

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:

a) m/s

b) km/h

Thanks guys.

2. 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.
Use the angle to find h when r=1.7

$\displaystyle 1.7tan(38)=1.328=h$

$\displaystyle V=\frac{\pi}{3}r^{2}h$

Differentiate w.r.t r, plug in dV/dt, r, and h and solve for dr/dt.