Question

Please help me with this question .GIven the equation:S = 144t - 16t^2

Answer 1

Given the equation:

`S=144t-16t^2`

Let's solve for the following:

• The time at which the ball is at its highest point.

To find the time at which the ball is at its highest point, apply the formula:

`t=-(b)/(2a)`

Rearrange the equation into a proper quadratic equation:

`S=-16t^2+144t`

Where:

a = -16

b = 144

Thus, we have:

`\begin{gathered} t=-(b)/(2a) \\ \\ t=-(-144)/(2(-16)) \\ \\ t=(-144)/(-32) \\ \\ t=4.5 \end{gathered}`

Therefore, the time at which the ball is at its highest point is 4.5 seconds.

• Estimate the height of the ball at that time.

To estimate the height of the ball at that time, substitute 4.5 for t and solve for S.

We have:

`\begin{gathered} S=144t-16t^2 \\ \\ S=144(4.5)-16(4.5)^2 \\ \\ S=648-16(20.25) \\ \\ S=648-324 \\ \\ S=324 \end{gathered}`

Therefore, the height of the ball at that time is 324 ft.

ANSWER:

• t =, ,4.5, s

,

• S =, ,324, ,ft