14. Roger is on a playground swing, and he is swinging back and forth in such a way that the height, h, in feet, of the swing off the ground is given by the equation h=3cos(3π/2t) +5, where t is in seconds. How many seconds elapses between two consecutive times that the swing is at its maximum height?

The time  seconds elapses between two consecutive times that the swing is at its maximum height  'h' = 2

 Step-by-step explanation:

Explanation:-

Step(i):-

Given function ....(i)

By using derivative formulas

Step(ii):-

Differentiating equation(i) with respective to 't'

 ...(ii)

Equating zero

on simplification , we get

now we use formulas

sin 0 = 0 and sinπ = 0

General solution

Cancellation 'π' on both sides, we get

Dividing '2' on both sides , we get

Again differentiating with respective to 't' , we get  

Put t= 3/2 and simplification

The maximum height

 seconds elapses between two consecutive times that the swing is at its maximum height  'h' = 2

Conclusion:-

The time  seconds elapses between two consecutive times that the swing is at its maximum height  'h' = 2

i got 86 for this

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