Cars on a certain roadway travel on a circular arc of radius r. In order not to rely on friction alone to overcome the centrifugal force, the road is banked at an angle of magnitude θ from the horizontal (see figure). The banking angle must satisfy the equation rg tan θ = v², where v is the velocity of the cars and g = 32 feet per second per second is the acceleration due to gravity. Find the relationship between the related rates dv/dt and dθ/dt.

Transcribed Image Text:

Ө Г