Please help me out my calculus problem!?

Question

A runner runs around a circular track of radius 100m at a constant speed of 7m/s. the runner's friend is standing at a distace 200m from the center of the track. how fast is the distace between the friends changing when the distacne between them is 200m?

Please! help me out!

Answer 1

The best thing I can think of follows:

The distance (d) covered = speed x time

speed = 7m/s

so d = 7t

This means t = d/7 = 1/7d

The derivative = 1/7d^-1

= 1/7d

The rate of change is the x co'ordinate (distance) through the derivative.

R.O.C = 1/7(200)

= 1/1400

= 0.0007 m/s

So I think the distance between them is changing at 0.0007 m/s when the distance is at 200m.


This is just what I think it is, that does NOT mean it is 100% correct, please consult with someone else, don't take my word for it.

Answer 2

Let X denote the position of the runner and Y of his friend. The distance XY changes at a rate which is 7m/s times the cosine of the angle between the line XY and the tangent at X of the circle.
Now determining this cosine is a simple exercise using Pythagore's theorem.