Answer to Question #158247 in Trigonometry for Tanner Bell

Question

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

Answer 1

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.

$$OA=99yd=297ft$$

Now, Nick is running at a speed of $11ft/sec$ for $30$ seconds.

So, Nick travelled $11\cdot30 ft=330ft$ for those $30$ seconds. (as distance= speed$\cdot$ time)

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

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

So, the total distance covered by Nick is

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

Therefore the total distance Nick travelled is $924ft$ .