Given the equation:
[tex]S=144t-16t^2[/tex]
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:
[tex]t=-\frac{b}{2a}[/tex]
Rearrange the equation into a proper quadratic equation:
[tex]S=-16t^2+144t[/tex]
Where:
a = -16
b = 144
Thus, we have:
[tex]\begin{gathered} t=-\frac{b}{2a} \\ \\ t=-\frac{-144}{2(-16)} \\ \\ t=\frac{-144}{-32} \\ \\ t=4.5 \end{gathered}[/tex]
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:
[tex]\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}[/tex]
Therefore, the height of the ball at that time is 324 ft.
ANSWER:
• t =, ,4.5, s
,
• S =, ,324, ,ft
