Arunner sprints around a circular track of radius 100 m at a constant speed of 7 mys. the runner’s friend is standing at a distance 200 m from the center of the track. how fast is the distance between the friends changing when the distance between them is 200 m?

Step-by-step explanation:

Let B represents the position of runner, A represents the position of the friend and C represents the position of centre of the circular track. ( shown  below ),

We need to find :

By the cosine law,

Differentiating with respect to t ( time ),

Now, by arc length formula,

Radius( say r ) × angle = arc length ( say l )

Differentiating w. r. t. t,

Here,

,

Now, again

We know that,

From equation (1), (2) and (3),

Hence, the distance between the friends changing with the rate of meter per sec.

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