the height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be…

the height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function (f(t)=-16t^{2}+48t), where (t) is the time in seconds since the rocket was shot and (f(t)) is the rockets height in feet. what is the maximum height the rocket reaches?\n16 ft\n36 ft\n48 ft\n144 ft

the height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function (f(t)=-16t^{2}+48t), where (t) is the time in seconds since the rocket was shot and (f(t)) is the rockets height in feet. what is the maximum height the rocket reaches?\n16 ft\n36 ft\n48 ft\n144 ft

Answer

Explanation:

Step1: Identify the function type

The function $f(t)=-16t^{2}+48t$ is a quadratic function in the form $y = ax^{2}+bx + c$, where $a=-16$, $b = 48$, $c = 0$.

Step2: Find the time of maximum height

The $t$-coordinate of the vertex of a quadratic function $y=ax^{2}+bx + c$ is given by $t=-\frac{b}{2a}$. Substitute $a=-16$ and $b = 48$ into the formula: $t=-\frac{48}{2\times(-16)}=\frac{48}{32}=\frac{3}{2}$ seconds.

Step3: Calculate the maximum height

Substitute $t = \frac{3}{2}$ into the function $f(t)=-16t^{2}+48t$. So $f(\frac{3}{2})=-16\times(\frac{3}{2})^{2}+48\times\frac{3}{2}=-16\times\frac{9}{4}+72=- 36 + 72=36$ feet.

Answer:

36 ft