A Ferris wheel 20 m in diameter has six cars spaced at equal intervals around it

Question

A Ferris wheel 20 m in diameter has six cars spaced at equal intervals around its circumference as shown. The figure shows a snapshot at t = 0. The expression for the height of car #3 versus time is: ^3(t) = (10 m) cos(omega t-pi/3). From the figures on the next page, choose the phasor diagram that best represents: The phasor y3 representing the height of car #3 versus time, and The phasor y2 representing the height of car #2 versus time, and The phasor y3 - y2 representing the height of car #3 above car #2 versus time. The height y of car #3 above car #2 can be written: (5 m )cos(omega t) (5m)(sin(omega t) (10m)cos(omega t)

Explanation / Answer

2)Let the total time period be T ,so w = 2*pi /T

the height of y3 = 10cos(wt-pi/3)

aat t= 0 the hieght will be 5m

the height of y2 wil be y2= 10cos( wt -2pi/3)

so, the the height difference can be written as ,

y3-y2

= 10cos(wt-pi/3) - 10cos(wt-2pi/3)

since ,

Cos(a -b) = cos a cos b + sin a sin b

so,

10cos(wt-pi/3) - 10cos(wt-2pi/3)

=10[ cos(wt)cos(pi/3)+ sin(wt)(sin(pi/3) - cos(wt)cos(2pi/3) -sin(wt)(sin(2pi/3) ]

=10 cos(wt)

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