A runner sprits around a circular track of radius 130 m at constant speed of 7 m

Question

A runner sprits around a circular track of radius 130 m at constant speed of 7 m/s. The runner's friend is standing at a distance 260 m from the center of the track. How fast is the distance between the friends changing when the distance between them is 260m? (Round to two decimal places) A runner sprits around a circular track of radius 130 m at constant speed of 7 m/s. The runner's friend is standing at a distance 260 m from the center of the track. How fast is the distance between the friends changing when the distance between them is 260m? (Round to two decimal places)

Explanation / Answer

Let Theta = angle formed by line from centre to runner with positive x-axis
Let s = distance along circular track where runner is located
and where s = 0 is at position (130,0)

Runner sprints at constant speed of 7m/sec . . . . ds/dt = 7

Formula for arc length:
s = r Theta
s = 130 Theta

Differntiate on both the sides with respect to t.
ds/dt = 130 dTheta/dt
7 = 130 dTheta/dt
dTheta/dt = 7/130

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Let (x,y) be runners position
x = r cos(Theta) = 130 cos(Theta)
y = r sin(Theta) = 130 sin(Theta)
x

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