Question

a toy car races along a circular track and is constantly 4 feet from the center of the race track. imagine an angle with a vertex at the center of the race track that subtends the car's path. (draw a diagram of this!) if the racecar travels 2 feet in the ccw direction along the track, what is the angle's measure in radians?

Answer 1

To find the angle's measure in radians subtended by a toy car's 2 feet path on a circular track with a 4 feet radius, the formula Δθ = s / r is used, yielding an angle of 0.5 radians.

Step-by-step explanation:

The student is asking about finding the angular measure in radians of a path traveled by a toy car along a circular track. Since the radius of the circular track is given as 4 feet and the distance traveled by the car is 2 feet, the calculation involves using the formula for the rotation angle, which is the arc length (s) divided by the radius (r).

Using the formula for the rotation angle:

Δθ = s / r

We plug in the values we know:

Δθ = 2 feet / 4 feet

Δθ = 0.5 radians

This is the measure of the angle in radians for the path traveled by the racecar.