A race car is driven around a circular track having a diameter of 4 miles at a speed of 120 miles per hour. In order to count completed circuits, a motion sensing counter is located at a fixed point adjacent to the track. How fast is the linear distance between the car and the counter increasing at the instant the car has travelled pi miles past the counter?

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anonymous · Answer

ok, i'm going to try to work this through. the entire distance of the racetrack is 4π, right? because the circumference is 2πr and r is 2. I don't know where the motion sensor is located, but it doesn't matter, so I will just put it at the top. So at π distance after the sensor, the linear distance is is a hypotenuse of the right triangle created (look at picture). Do you see it now? |dw:1356154996528:dw|