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.
