Question

Alice is skiing along a circular ski trail that has a radius of 2.5 km. She starts at the 3-o'clock position and travels in the CCW direction. Alice stops sking when she is 2.251 km to the right and 1.087 km above the center of the ski trail. Imagine an angle with its vertex at the center of the circular ski trail that subtends Alice's path.

a. How many radians has the angle swept out since Alice started skiing?


b. How many km has Alice skied since she started skiing?

Answer 1

Find the given attachment

Answer 2

a)
`\theta = 0.143\,rad`, b)
`\Delta s = 0.358\,km`

Explanation:

a) The change in angular position is:

`\theta = \tan^(-1) (1.087\,km)/(2.251\,km)`

`\theta = 0.143\,rad`

b) The distance travelled by Alice is:

`\Delta s = \theta \cdot r`

`\Delta s = (0.143\,rad)\cdot (2.5\,km)`

`\Delta s = 0.358\,km`