You go to an amusement park with your friend Betty, who wants to ride the 80-m-d

Question

You go to an amusement park with your friend Betty, who wants to ride the 80-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 ?

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?

Explanation / Answer

Here, let's take horizontal as the x axis

and vertical as the y axis

for the initial position

ri = -40 j m

for the final speed ,

rf = 40 * (sin(40) i - j *cos(40)) = 25.7 i - 30.6 j m

for the displacement vector

r = rf - ri

r = 25.7 i - 30.6 j - (-40 )j

r = 25.7 i + 9.4 j

magnitude of displacment vector = sqrt(25.7^2 + 9.4^2)

magnitude of displacment vector = 27.4 m

part B)

direction of her displacement = arctan(9.4/25.7)

direction of her displacement = 20 degree

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