A shortstop makes an error by dropping the ball. As the ball drops, its height [tex](h)[/tex] in feet, as a function of time [tex](t)[/tex], is modeled by [tex]h(t) = -16t^2 + 3[/tex]. A slow-motion replay of the error shows the play at half speed. What function describes the height of the ball in the replay? (Hint: The function squares the time, so half the time is also squared in the new function.)

A) [tex]h(t) = -16(0.5t)^2 + 1.5[/tex]
B) [tex]h(t) = \frac{-16t^2 + 3}{2}[/tex]
C) [tex]h(t) = -16\left(\frac{t}{2}\right)^2 + 3[/tex]
D) [tex]h(t) = -8t^2 + 3[/tex]

c because the time is being cut in half

Answered by abbeykitch | 2024-06-10

The correct function that describes the height of the ball on a replay that runs at half speed is h(t) = -16(t/2)^2 + 3. This is because the time in the original function enters as a square, so it must be halved before being** squared.** ;

Answered by JohnEvergreen | 2024-06-18

The function that describes the height of the ball in the half-speed replay is h ( t ) = − 16 ( 2 t ​ ) 2 + 3 , which corresponds to option C. This adjustment accounts for the fact that the time in the original function is squared. Therefore, substituting 0.5 t into the original height function is necessary for accurate representation.
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Answered by JohnEvergreen | 2024-10-01