To determine which equation correctly models the ball's height as a function of time, we can use the given formula for the height of a projectile:
[tex]\[ h(t) = -16t^2 + v_0 t + h_0 \][/tex]
Here's a step-by-step solution:
1. Identify Initial Height ( [tex]\( h_0 \)[/tex] ) and Initial Speed ( [tex]\( v_0 \)[/tex] ):
- The problem states that the ball starts at a height of 2 feet.
- Therefore, [tex]\( h_0 = 2 \)[/tex] feet.
- The initial speed with which the ball is launched is 120 feet per second.
- Thus, [tex]\( v_0 = 120 \)[/tex] feet/second.
2. Substitute the Given Values into the Formula:
- Plugging in the initial height [tex]\( h_0 = 2 \)[/tex] and initial speed [tex]\( v_0 = 120 \)[/tex]:
[tex]\[
h(t) = -16t^2 + 120t + 2
\][/tex]
3. Verify the Correct Equation:
- Now, we match our derived equation [tex]\( h(t) = -16t^2 + 120t + 2 \)[/tex] with the provided options:
- A. [tex]\( h(t) = -16t^2 - 2t + 120 \)[/tex]
- B. [tex]\( h(t) = -16t^2 + 120t + 2 \)[/tex]
- C. [tex]\( h(t) = -16t^2 + 2t + 120 \)[/tex]
- D. [tex]\( h(t) = -16t^2 - 120t - 2 \)[/tex]
4. Conclusion:
- The equation [tex]\( h(t) = -16t^2 + 120t + 2 \)[/tex] corresponds to option B.
Hence, the correct equation that models the ball's height as a function of time is:
[tex]\[ \boxed{B} \][/tex]
