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The equation for a projectile's height versus time is [tex]h(t) = -16 t^2 + v_0 t + h_0[/tex].

A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. Which equation correctly models the ball's height as a function of time?

A. [tex]h(t) = -16 t^2 + 120 t + 2[/tex]

B. [tex]h(t) = -16 t^2 + 2 t + 120[/tex]

C. [tex]h(t) = -16 t^2 - 2 t + 120[/tex]

D. [tex]h(t) = -16 t^2 - 120 t - 2[/tex]

Sagot :

GinnyAnswer
To find the correct equation that models the ball's height as a function of time, let's break down the given information and apply it to the general equation for height of a projectile.

The general formula for the height of a projectile is:
[tex]\[ h(t) = -16t^2 + v_0 t + h_0 \][/tex]

We know:
- The initial height [tex]\( h_0 \)[/tex] is 2 feet.
- The initial speed [tex]\( v_0 \)[/tex] is 120 feet per second.

Substituting these values into the general formula, we get:
[tex]\[ h(t) = -16t^2 + 120t + 2 \][/tex]

So, the correct equation of the ball's height as a function of time is:
[tex]\[ h(t) = -16t^2 + 120t + 2 \][/tex]

Now, let's compare this with the given options:
A. [tex]\( h(t) = -16t^2 + 120t + 2 \)[/tex]
B. [tex]\( h(t) = -16t^2 + 2t + 120 \)[/tex]
C. [tex]\( h(t) = -16t^2 - 2t + 120 \)[/tex]
D. [tex]\( h(t) = -16t^2 - 120t - 2 \)[/tex]

The correct option is:
A. [tex]\( h(t) = -16t^2 + 120t + 2 \)[/tex]

Hence, option A is the correct model for the ball's height as a function of time.
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