a zeppelin floating tranquilly alternates between a height of 1500m and 900 m according to a model of a sin function...More below The zepellin reaches maximum height every 75 minutes. Assuming the observer starts watching the zepellin when it is at a height of 900 m, and the observer spends the afternoon (5 full hours) picknicking and enjoying the mighty balloon's flight ...determine the equation to model the flight observed by the picknicker 

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lets assume the sine function is in the following form,

`y = Asin(bt+c)+D`

now according to the data, the minimum height is 900 m and maximum height is 1500 m. These two values corresponds to the minimum and maximum values that sine can get, which are -1 and +1 respectively.


900 = A(-1)+D

`900 = -A+D ` ------1


1500 = A(1)+D

`1500 = A+D` ------2


solving 1 and 2 you will get,

A = 300 and D = 1200.

So the equations reduces to,

`y = 300sin(bt+c)+1200`

but we know at t = 0, y = 900 (At the lowest point)


`900 = 300 sin(c)+1200`

This gives,

`sin(c) = -1`

`c = sin^(-1)(-1)`

`c = -pi/2`

The other thing we know is, it has period of 75 minutes,

then, it reaches its first maximum at 75/2 minutes which is 1500 m

`1500 = 300sin(b*(75/2) -pi/2)+900`

`300sin(b*(75/2) -pi/2) = 300`

`sin(b*(75/2) -pi/2) = 1`

`b*(75/2) -pi/2 = pi/2`

`b*(75/2) = pi`

`b = (2pi)/75`

Therefore teh required equation is,

`y = 300sin((2pit)/75-pi/2)+1200`

Approved by eNotes Editorial Team