It is about trigonometry ?

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Answer 1 · 2018-05-01T23:10:27

Given that the height of the rider from the ground on the wheel after t th sec of his start from ground follows the following relation

#h=60(1-cos(kt)# m.

Where #k# is a constant and #t# is the time in minute.

At #t=0#

#h=60(1-cos(k*0)=0# m.

(1)

Again

#h=60(1-cos(k*t))# m.

The greatest or maximum height of the rider will be when cos(kt) is minimum i.e. #cos(kt)=-1#

So #h_"max"=60(1-(-1))=120# m

Wheel undergoes one complete rotation in 30 min.

(2) So when #t=30# min, #h=0#

#0=(1-cos(k*30)#

#=>cos(k*30)=1=cos(2pi)#

#=>k=(2pi)/30=pi/15#

(3) when #h=90# m let time be #T# min

We have

#90=60(1-cos(pi/15*T)#

#=>90/60=(1-cos(pi/15*T)#

#=>3/2=(1-cos(pi/15*T)#

#=>cos(pi/15*T)=1-3/2=-1/2=cos((2pi)/3)#

So #T=(2pi)/3*15/pi=10# min