# Please help me with this problem?

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John and Peter take a ride in a ferris wheel. John enters first, Peter after

6 minutes. Measuring from the time that Peter enters, the height of John's cabin as a function of time is given by: #h_J(t)=42+sin((pit)/12)# .

The height of Peter's cabin is given by #h_P(t)=42-cos((pit)/12)# .

Time is measured in minutes, height in meters.

At time interval #[0,24]# , for which #t# do we have #h_P(t)>h_J(t)# ?

John and Peter take a ride in a ferris wheel. John enters first, Peter after

6 minutes. Measuring from the time that Peter enters, the height of John's cabin as a function of time is given by:

The height of Peter's cabin is given by

Time is measured in minutes, height in meters.

At time interval

##### 1 Answer

#### Answer:

#### Explanation:

Given:

#h_J(t) = 42+sin((pit)/12)#

#h_P(t) = 42-cos((pit)/12)#

We want to know when:

#h_P(t) > h_J(t)#

That is:

#42-cos((pit)/12) > 42+sin((pit)/12)#

Subtract

#0 > sin((pit)/12) + cos((pit)/12)#

In order for the right hand side to be zero, we would require

The angles at which

Of these, the quadrants in which

Hence the sign of

Note that

Hence the interval for which

#(3pi)/4 < (pit)/12 < (7pi)/4#

Multiply through by

#9 < t < 21#