Answered

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Stephen kicked a ball inside. The equation that represents the height h in feet of the ball after being kicked and elapsed amount of time t in seconds

Sagot :

MrRoyal

Answer:

The maximum height of the ball is: 14.0625ft

Step-by-step explanation:

The missing information is:

[tex]h(t) = 30t - 16t^2[/tex]

Required

The maximum height the ball attained

First, we calculate the time to reach the maximum height.

For a function: [tex]h(t) = at^2 + bt + c[/tex]

The maximum is: [tex]t = \frac{-b}{2a}[/tex]

So, the maximum of [tex]h(t) = 30t - 16t^2[/tex] is:

[tex]t = \frac{-b}{2a}[/tex]

Where

[tex]a = -16; b = 30[/tex]

So:

[tex]t = -\frac{30}{2*-16}[/tex]

[tex]t = -\frac{30}{-32}[/tex]

[tex]t = \frac{30}{32}[/tex]

[tex]t = 0.9375[/tex]

The maximum height is then calculated as:

[tex]h(t) = 30t - 16t^2[/tex]

[tex]h(0.9375) = 30 * 0.9375- 16 * 0.9375^2[/tex]

[tex]h(0.9375) = 28.125- 14.0625[/tex]

[tex]h(0.9375) = 14.0625[/tex]

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