An auto race takes place on circular track. A car completes one lap in time of 26.4s, with an average tangential speed of 42.9 m/s. Find the radius of the track.
To find the radius of the track, we can use the formula for the circumference of a circle. The average tangential speed of the car is equal to the distance traveled divided by the time taken.
Average tangential speed = Distance traveled / Time taken
42.9 m/s = (2πr) / 26.4s
Simplifying the equation, we have:
42.9 m/s = (2πr) / 26.4s
To isolate r, we can multiply both sides of the equation by 26.4s and divide by 2π:
r = (42.9 m/s * 26.4s) / (2π)
r = (1131.6 m^2/s) / (2π)
Now, we can calculate the radius using a calculator or approximation for π:
r ≈ (1131.6 m^2/s) / (6.28)
r ≈ 180.45 m
Therefore, the radius of the track is approximately 180.45 meters.