Calculus I, Math 170 Final Exam Solutions Spring 2009 Directions ...

(13) Car A is traveling due west toward school at a speed of 55 mph. Car B is traveling due
north away from school at a speed of 40 mph. Let x be the distance between Car A and
the school at time t, and let y be the distance between Car B and the school at time t, as
shown in the figure.
y B
(a) (2 points) Find the distance in miles between the cars when x = 20 miles and y = 15
miles. A school d x
(b) (8 points) Find the rate of change, in mph, of the distance between the two cars when
x = 20 miles and y = 15 miles.
(c) (6 points) Let θ be the angle at Car A in the above figure. Find θ ′ , the rate of change
of θ with respect to time when x = 20 and y = 15. Based upon your answer, is θ
increasing?