With reference to the attached scenario: The 100 meter diameter wheel needs to be designed so that it rotates at a constant rate and every complete revolution takes 15 minutes. The wheel has been installed in a vertical plane and the lowest seat is 2m above the ground surface. Each ride consists of only one full rotation. 1) You are required to obtain an expression for the height of a rider above the ground in terms of both the angle radians the wheel rotates through and the time t, assuming that the rider is initially at a seat that is 2m above the ground surface at the start of the wheel’s journey. 2) Find a general expression for the rate of ascend for this rider in terms of both the angle of rotation and time. 3) Determine how fast this rider is moving vertically when 560 sec and state whether it is ascending or descending. Justify your answer. 4) Find a further general expression for the horizontal displacement of the rider from its initial position with respect to both time and angle of rotation and hence determine the speed of the rider when 180 sec.
With reference to the attached scenario:
The 100 meter diameter wheel needs to be designed so that it rotates at a constant rate and every complete revolution takes 15 minutes. The wheel has been installed in a vertical plane and the lowest seat is 2m above the ground surface. Each ride consists of only one full rotation.
1) You are required to obtain an expression for the height of a rider above the ground in terms of both the angle radians the wheel rotates through and the time t, assuming that the rider is initially at a seat that is 2m above the ground surface at the start of the wheel’s journey.
2) Find a general expression for the rate of ascend for this rider in terms of both the angle of rotation and time.
3) Determine how fast this rider is moving vertically when 560 sec and state whether it is ascending or descending. Justify your answer.
4) Find a further general expression for the horizontal displacement of the rider from its initial position with respect to both time and angle of rotation and hence determine the speed of the rider when 180 sec.
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