if a projectile is fired straight upward from the ground with an initial speed of 160 feet per second, then…

if a projectile is fired straight upward from the ground with an initial speed of 160 feet per second, then its height h in feet after t seconds is given by the function h(t)= - 16t² + 160t. find the maximum height of the projectile. the maximum height of the projectile is (simplify your answer.)

if a projectile is fired straight upward from the ground with an initial speed of 160 feet per second, then its height h in feet after t seconds is given by the function h(t)= - 16t² + 160t. find the maximum height of the projectile. the maximum height of the projectile is (simplify your answer.)

Answer

Explanation:

Step1: Identify the function type

The height - function $h(t)=-16t^{2}+160t$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 160$, and $c = 0$.

Step2: Find the time $t$ at the vertex

The $t$ - value of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by the formula $t=-\frac{b}{2a}$. Substitute $a=-16$ and $b = 160$ into the formula: $t=-\frac{160}{2\times(-16)}=\frac{160}{32}=5$.

Step3: Find the maximum height

Substitute $t = 5$ into the height - function $h(t)=-16t^{2}+160t$. $h(5)=-16\times5^{2}+160\times5=-16\times25 + 800=-400+800 = 400$.

Answer:

400