Question

h(t) = -16t² + 27t + 12
what is the velocity?
what is the starting height?
drag these tiles and drop them in the correct blank above
-16 12 27

Explanation:

Step1: Analyze velocity from height function

The height function for a projectile is generally \( h(t) = -16t^2 + vt + s \), where \( v \) is velocity and \( s \) is starting height. In \( h(t)=-16t^2 + 27t + 12 \), the coefficient of \( t \) is velocity. So velocity is \( 27 \).

Step2: Analyze starting height from height function

In the height function \( h(t) = -16t^2 + vt + s \), \( s \) is the starting height (when \( t = 0 \), \( h(0)=s \)). For \( h(t)=-16t^2 + 27t + 12 \), when \( t = 0 \), \( h(0)=12 \), so starting height is \( 12 \).

Answer:

Velocity: \( 27 \)
Starting height: \( 12 \)