A circle of radius 1 is placed on an incline where point P, a point on the circle, has the coordinates `(-5, -5)`. The circle is rolled up the incline, and once the circle hits the origin, the circle is then rolled horizontally along the x - axis to the right. What is the x - coordinate of the point where P touches the incline or the x - axis for the fifth time (not including the starting point) ?

Options

A. `8.64`
B. `17.27`
C. `24.34`
D. `27.49`

Answer

C

Explanation

With 5 rotations, the circle covers a total distance equal to 5 times the circumference. The circumference of a circle of radius 1 is `2pi`, so 5 times that is `10pi`. Of that total distance `10pi, 5sqrt(2)` is on the incline.
The other `10 pi - 5sqrt(2)` is the distance traveled along the x - axis, so the x - coordinate of the endpoint is `10pi - 5sqrt(2)~~ 24.34`.