The Beijing wheel, soon to be the world's largest Ferris wheel at 208 metres tall, will have 48 air conditioned observation capsules evenly spaced out alon

Question

The Beijing great wheel soon to be the world's largest Ferris wheel at 208 metres tall, will have 48 air conditioned observation capsules evenly spaced out along the 622m metal ring. You will reach the top 3 times in a one hour ride. Determine the first four consecutive times that you will pass 100m during your ride.

Answer 1

First we need to find the diameter and radius of the ferris wheel by noting that the 622m is the circumference of the ferris wheel.  Since C= πd we find that d = C/Π = 622/Π ≈198m and r = d/2 = 99m.  The equation that describes the y coordinate for counterclockwise motion on a circle or radius r centered at the origin is y=r*sin(ωt)  where ω=2πf.  We find the frequency by noting that the wheel make 3 revolutions per hour so f = 3/1 = 3 cycles per hour and ω=2π(3)=6π therefore

 

y=99sin(6πt)

 

The starting point, t=0, for y is (99,0).  We need to shift this point bakc by -π/2, where a person gets on the wheel.

 

y=99sin(6πt - π/2)

 

 I cannot draw the circle in this word editor you will need to that.  To find an expression for the height above the ground we need to place the origin at ground level.  The wheel sits on some platform that keeps it off the ground.  To find the platforms height we note that the overall height is 208m.  Platforms height = overall height - diameter = 208 - 199 = 9m.  We shift our center up by 9 meter.  Since the radius is 99m we shift y up vertically by 99+9=108 , to get h

 

h = y+108 = 99sin(6πt - π/2) + 108

 

Now set h = 100 and solve for t

See if you can finish the problem.  If not send me comment.