The figure in Exercise 69 shows the particle traveling away from the sensor, which may have influenced your solution (we expect you used the inverse sine function). Suppose instead that the particle approaches the sensor (see figure). How would this change the solution? Explain the differences in the two answers.

Data from Exercise 69

A particle travels clockwise on a circular path of diameter D, monitored by a sensor on the circle at point P; the other endpoint of the diameter on which the sensor lies is Q (see figure). Let θ be the angle between the diameter PQ and the line from the sensor to the particle. Let c be the length of the chord from the particle's position to Q.

a. Calculate dθ/dc.

b. Evaluate 

Transcribed Image Text:

D Sensor Particle OP dc| c=