the function h(t)= - 16t² + 96t + 10 models the path of a projectile. fill in the blanks to complete the…

the function h(t)= - 16t² + 96t + 10 models the path of a projectile. fill in the blanks to complete the statements below.\nby inspecting the function, you can tell that the initial height of the projectile is 10 ft and the initial velocity is 96 ft/s.\nthe projectile reaches a maximum height of ft at time s.

the function h(t)= - 16t² + 96t + 10 models the path of a projectile. fill in the blanks to complete the statements below.\nby inspecting the function, you can tell that the initial height of the projectile is 10 ft and the initial velocity is 96 ft/s.\nthe projectile reaches a maximum height of ft at time s.

Answer

Explanation:

Step1: Identify the form of the function

The function $h(t)=-16t^{2}+96t + 10$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 96$ and $c = 10$.

Step2: Find the time of maximum - height

The time $t$ at which the projectile reaches its maximum height is given by the formula $t=-\frac{b}{2a}$. Substitute $a=-16$ and $b = 96$ into the formula: $t=-\frac{96}{2\times(-16)}=\frac{-96}{-32}=3$.

Step3: Find the maximum height

Substitute $t = 3$ into the function $h(t)=-16t^{2}+96t + 10$. $h(3)=-16\times3^{2}+96\times3 + 10=-16\times9 + 288+10=-144 + 288+10=154$.

Answer:

The projectile reaches a maximum height of $154$ ft at time $3$ s.