Question

Wheel that, as you face it, rotates counterclockwise.part A) What is the magnitude of her displacement vector when the wheel has rotated by an angle of 40 degrees?Express your answer with the appropriate

You go to an amusement park with your friend Betty, who wants to ride the 70-m-diameter Ferris wheel. She starts the ride at the lowest point of a wheel that, as you face it, rotates counterclockwise.
part A) What is the magnitude of her displacement vector when the wheel has rotated by an angle of 40 degrees?
Express your answer with the appropriate units.
part B) What is the direction of her displacement vector when the wheel has rotated by an angle of 40°, measured counterclockwise from the horizontal?

Answer 1

The magnitude of Betty's displacement vector after rotating 40 degrees on a 70-meter diameter Ferris wheel is 24.43 meters. The direction of her displacement vector is 40 degrees measured counterclockwise from the horizontal.

Step-by-step explanation:

When Betty rides a Ferris wheel with a 70 meter diameter and starts at the lowest point, with the wheel rotating counterclockwise, we can calculate her displacement after a 40-degree rotation. The displacement in this context refers to the vector pointing from her starting position to her new position.

Part A) The magnitude of her displacement vector after a 40-degree rotation can be found using the arc length of a circle segment, which is:

• s = rθ, where s is the arc length, r is the radius, and θ is the angle in radians.

To find the displacement, we need to convert the angle to radians (40 degrees × (π/180) = 0.698 radians) and use the radius of the Ferris wheel, which is half of its diameter (70m/2 = 35m).

• Displacement magnitude = 35m × 0.698 = 24.43m

The units are meters, as displacement is a length measure.

Part B) The direction of her displacement vector, when measured counterclockwise from the horizontal, is simply 40 degrees, as this is the angle of rotation from the start point at the bottom of the Ferris wheel.