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A town has a fireworks display, where fireworks are set off from a bridge over a lake. The function h (t) = -16t2 + 150t + 10.5 represents

the approximate height of each firework, in feet, t seconds after it is launched.

Approximately when do the fireworks reach their maximum height?

1 Answer

7 votes

Answer:

h(t) = 4.68 seconds

Explanation:

The function that represents the height of each firework in feet is :


h (t) = -16t^2 + 150t + 10.5 .....(1)

We need to find the time the fireworks take to reach their maximum height. For maximum height,

dh/dt = 0

So,


(d)/(dt)(-16t^2 + 150t + 10.5 )=0\\\\-32t+150=0\\\\t=(150)/(32)\\\\t=4.68\ s

Put t = 4.68 in equation (1).


h (t) = -16(4.68)^2 + 150(4.68)+ 10.5\\\\h(t)=362.06\ text{feet}

So, the fireworks will take 4.68 seconds to their maximum height.

User Shanebonham
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