Question #158247

Nick runs around the perimeter of a circular track at 11 ft/sec. The track has a radius of 99 yd. After 30 seconds, Nick turns and runs to the center of the track along a straight (radial) line. Upon reaching the center, he turns and runs away along a different radial line to his starting position on the perimeter.

How far has Nick traveled once he has returned to his starting position?

distance =  feet


1
Expert's answer
2021-01-26T04:43:32-0500


Here,

we have a circle centered at O and A is the starting point of Nick, with OA as the radius of the circle.

We know OA=99yd=297ft.

Then Nick runs for 30 seconds till B on the circumference and then returns to O and then back to A via

a radial line.



OA=99yd=297ftOA=99yd=297ft

Now, Nick is running at a speed of 11ft/sec11ft/sec for 3030 seconds.

So, Nick travelled 1130ft=330ft11\cdot30 ft=330ft for those 3030 seconds. (as distance= speed\cdot time)


\therefore AB=330ft\overgroup{AB}=330ft


Now, he goes to the center via OB=297ft297ft and then further to his starting point A via OA=297ft297ft .


So, the total distance covered by Nick is


AB+BO+OA=330+297+297=924ft\overgroup{AB}+\overline{BO}+\overline{OA}\\ =330+297+297=924ft

Therefore the total distance Nick travelled is 924ft924ft .


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