Nahee is running around the circular track with equation x2+y2=6400 at a speed of 2.8 meters per second. She starts at the point (0,80) and runs counterclockwise. What are Nahee's coordinates after she has been running for 13 minutes?

Question

aum · Answer

x^2 + y^2 = 6400
x^2 + y^2 = 80^2
The radius of the circle is 80 meters.

Distance run in 13 minutes = 2.8 * 13 = 36.4 meters along an arc of a circle.

Arc length = r * theta = 80 * theta = 36.4
theta = 36.4 / 80 = 0.455 radians.

Starting point is (0,80) which is long the y-coordinate which makes an angle of pi/2 radians with the x-axis.  From that starting point an angle of 0.455 radians is run counterclockwise.  So the final angle with the x-axis is pi/2 + 0.455 = 2.0258 radians.

Final x-coordinate = 80 * cos(2.0258 radians) = ?
Final y-coordinate = 80 *  sin(2.0258 radians) = ?

(Make sure your calculator is set to radians mode and not degree mode).