GROUP PROJECT Modeling a Double Ferris Wheel OBJECTIVE: To find w hode for the h

Question

GROUP PROJECT Modeling a Double Ferris Wheel OBJECTIVE: To find w hode for the height of a rider on a double Ferris wheel. In 1939, Jobn Courtncy inventod the irat double Ferris whcel, called a Sky Wheek consisting of two smaller wheels spinning at the ends of a rolating arm For this project, we win model a double rerris wheel with 50-foot arm that is spinning at a rate of 3 revolntions per minue in a counterclockwise direction. The center o the arm is 44 feet abave the ground. 32 feet, and the wheels torn at a rate of S revolutions per misute in a clodkwisc direction. A diagram of The diaimeter of each wheel is shown in Figure 1. M is the midpoint of the situation is the arm, and O is the center of the lower wheel. Assume the rider is initially at point P on the wheel. Determine the lengths of MO, OP, and MG Figure 2 shows the location of the rider after a short amount of time has passed. The arm has rotated counterclockwise through an angle 8, while the wheel has rotated clockwise through an angle relative to the direction of the arm. Point P shows the cureot position of the rider, and the height of the rider is h Ho- 25 P Ilo Figure 2 Figure 1 Find angle QOP in terms of and . Use right triangle trigonometry to find lengths a and b, and then the height of the rider h, in terms of e and 3

Explanation / Answer

1.)

we have to find MO , OP and MG

so first MO

M is the midpoint of that 50 feet arm so MO will be half of that so

MO = 25 feet

Now OP

OP is the radius of the wheel

diameter of wheel is 32 feet

radius = 32 / 2 = 16 feet

OP = 16 feet

Now MG

MG is the height of the center point (M) of the arm from the ground which is given 44 feet so

MG = 44 feet

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