Question

Nahee is running around the circular track with equation x2+y2=10000 at a speed of 2.9 meters per second. She starts at the point (0,100) and runs counterclockwise. What are Nahee's coordinates after she has been running for 13 minutes?

Answer 1

The coordinates are (58.1, - 81.4).

Explanation:

The distance traveled by Nahee after 13 minutes at the rate of 2.9 m/sec along the arc of the circle with equation x² + y² = 100², will be (13 × 60 × 2.9) = 2262 m

Now, the perimeter of the circle is 2πr =
`2 * (22)/(7)* 100 = 628.57` m

Therefore, after traveling three full circles and a half-circle the remaining arc length will be [2262 - (628.57 × 3) - (628.57 ÷ 2)] = 62 m

Therefore, Nahee will finish his run in the fourth quadrant.

Now, the angle made by the arc length of 62 m at the center will be =
`(360)/(628.57)* 62 = 35.512^(\circ)`

So, the angle made with positive x-axis will be (90° - 35.521°) = 54.488°

Now, the coordinates of the finishing point are (x,-y) = (rCos 54.488°, - rSin 54.488°) = (58.1, - 81.4) (Answer)