STATEMENT OF PROBLEM

A small mass is moving along the circle x^2 + y^2 = 25 (distances in centimeters) at a rate of 2 cm/sec. The mass begins at the top of the circle, i.e. at point (0, 5) cm, and moves down the side of the circle in the first quadrant, i.e. x >0 and y> 0) until it stops at the point (5, 0) cm.

A camera sits at point (10, 1) cm and we wish to aim the camera at the mass to capture the motion of the mass.

(a) When will the mass arrive at the point (5, 0) cm?

(b) Describe the motion of the mass as a position vector

p(t) = (x(t), y(t)).

(c) When will the camera first "see" the mass.

(d) Let theta be the angle which the line of site of the camera when focused on the mass on the circle makes with the horizontal. Write theta as a function of time t. Plot theta(t).

(e) Determine when the angular velocity theta'(t) and the angular acceleration theta''(t) are greatest and obtain these values.