Question

Derek is skiing on a circular ski trail that has a radius of 0.6 km. Derek starts at the 3-o'clock position and travels 2.4 km in the counter-clockwise direction.
a. How many radians does Brian sweep out?
b. When Brian stops skiing, how many km is Brian to the right of the center of the ski trail?
c. When Brian stops skiing, how many km is Brian above of the center of the ski trail?

Answer 1

Answer:

a) Brain sweep out 4 radians

b) Brian is -0.3922 km to the right of the center of the ski trail

c) Brian is -0.4541 km above of the center of the ski trail

Step-by-step explanation:

Given the data in the question;

circular ski trail radius = 0.6 km

Derek starts at the 3-o'clock position and travels 2.4 km in the counter-clockwise direction.

a) How many radians does Brian sweep out?

arc length = 2.4 km

from the diagram;

arc length = rθ

θ = arc length / r

θ = 2.4 / 0.6

θ = 4 radians

Therefore, Brain sweep out 4 radians

b) When Brian stops skiing, how many km is Brian to the right of the center of the ski trail?

from the diagram;

x = rcosθ

we substitute

x = 0.6 × cos(4)

x = 0.6 × -0.65364

x = -0.3922 km

Therefore Brian is -0.3922 km to the right of the center of the ski trail

c) When Brian stops skiing, how many km is Brian above of the center of the ski trail?

from the diagram;

m = rsinθ

m = 0.6 × -0.7568

m = -0.4541 km

Therefore, Brian is -0.4541 km above of the center of the ski trail