Question

5 the function $h(t) = -16t^2 + 32t + 24$ models the height h, in feet, of a ball t seconds after it is thrown straight up into the air.
the initial velocity is
the initial height of the ball is

Explanation:

Step1: Recall projectile height form

The standard form for vertical projectile height is $h(t) = -16t^2 + v_0t + h_0$, where $v_0$ = initial velocity, $h_0$ = initial height.

Step2: Match to given function

Given $h(t) = -16t^2 + 32t + 24$. Compare terms:

• Coefficient of $t$ is $v_0 = 32$
• Constant term is $h_0 = 24$

Answer:

The initial velocity is $\boldsymbol{32}$ feet per second
The initial height of the ball is $\boldsymbol{24}$ feet