A group of students is tracking a friend, Sam, who is riding a Ferris Wheel. They know that Sam reaches a maximum height of 15m and............the minimum height of 2m. The Ferris wheel completes...

A group of students is tracking a friend, Sam, who is riding a Ferris Wheel. They know that Sam reaches a maximum height of 15m and.......

.....the minimum height of 2m. The Ferris wheel completes two full revolutions in 3 minutes. Starting at the lowest point, determine an equation that gives Sam's height 'h' in meters in 't' seconds?

Asked on by islnds

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

This can be done using angular motion.

The Ferris wheel starts at the bottom point and complete two revolutions in 3min.

Using angular motion equations

`theta = omega_0t+1/2xxalphaxxt^2`

`omega_0 = 0`

`theta = 2xx2pi = 4pi`

`t = 3min = 180s`

 

Therefore;

`alpha = (2xx4pi)/(180^2) = 0.00077(rad)/s^2`

 

It is given that highest and lowest positions located 15m and 2m respectively. So the diameter of the Ferris wheel is (15-2) = 13m

 

Let us say the wheel is at an angle of theta from the bottom vertical at time t.

At this point;

Height h from bottom point `= 13/2- (13/2)costheta`

 

`theta = omega_0t+1/2xxalphaxxt^2`

 

`theta = 1/2xx0.00077xxt^2`

`theta = 0.000388t^2`

 

Height h from bottom point `= 13/2- (13/2)costheta`

Height h from bottom point `= 13/2- (13/2)cos(0.000388t^2)`

 

This is the height from the bottom point which is above 2m from ground.

Height from ground `= 2+13/2- (13/2)cos(0.000388t^2)`

Height from ground `= 8.5-6.5cos(0.000388t^2)`

 

 

Assumption

The Ferris wheel starts from rest at bottom point.

 

Sources:

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