Question

A skier skis CCW along a circular ski trail that has a radius of 1.9 km. She starts at the northern most point of the trail and travels at a constant speed, sweeping out 3.1 radians per hour. Let t represent the number of hours since she started skiing. Write an expression in terms of t to represent the number of radians that would need to be swept out from the East side of the ski trail (3 o'clock position) to reach the skier's current position. Write an expression in terms of t to represent the skier's distance East of the center of the circular ski trail (in km). Write an expression in terms of t to represent the skier's distance North of the center of the circular ski trail (in km).

Answer 1

The expressions of the number of radians can be expressed in the ways below.

How to write the expressions

The radius = 1.9 km

The angular speed = 3.1 radians per hour

a. The expression of t from the number of radians

θ = π/2 + 3.1t

b. Expression from the East

x = rcosθ

= 1.9cos(π/2 + 3.1t)km

c. Expression from the north of the center

= rsinθ

= 1.9sin((π/2 + 3.1t)km

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