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A fountain launches a stream of water directly out of a pool at a vertical speed of 48 feet per second. The water shoots up and then falls back into the pool. The height, h, of the water at time t, in seconds, is given by the equation h = –16t 2 + 48t. The greatest height of the water above the pool is

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Answer:

36 feet.

Step-by-step explanation:

h = -16t² + 48t .......... (1)

The above equation relates the height h, in feet of the water at time t, in seconds.

Now, condition for greatest height is [tex]\frac{dh}{dt} = 0[/tex] ......... (2)

So, differentiating equation (1) with respect to t we get, -32t + 48 = 0 {From condition (2).

⇒ t = 1.5 seconds

So, the greatest height is = -16 (1.5)² + 48 (1.5) = 36 feet. (Answer)

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