A standard 400 meter running track has semi-circles at each end. The radius of the inside lane of each semi-circle is 36.5 meters. The diagram shows one end of the track.
a. How many radius lengths mark-off the entire arc length of a semi-circular end of the track? Give an exact result
b. What's the distance in meters around the semi-circle in the inside lane? Enter an expression that gives an exact result.
Suppose from the starting line at coordinates (36.5, 0), you run 65 meters counterclockwise in the inside lane. (Note this is not the situation depicted in the diagram.) Round your answers to the nearest hundredth.
c. In your final position, how many radius lengths are you
above the horizontal diameter?
to the right of the vertical diameter?
d. Find the coordinates of your final position, rounded to the nearest hundredth of a meter.
e. Suppose you ran a distance of s meters from the starting line, where s is at most the arc-length of the full semicircle. Write expressions for the coordinates of your final position.