question a rocket is launched in the air. its height in feet is given by h(t)= -16t² + 56t where t…

question a rocket is launched in the air. its height in feet is given by h(t)= -16t² + 56t where t represents the time in seconds after launch. how many seconds have gone by when the rocket is at its highest point? answer: attempt 1 out of 2 seconds submit answer

question a rocket is launched in the air. its height in feet is given by h(t)= -16t² + 56t where t represents the time in seconds after launch. how many seconds have gone by when the rocket is at its highest point? answer: attempt 1 out of 2 seconds submit answer

Answer

Answer:

$\frac{7}{4}$

Explanation:

Step1: Identify the function type

The height function $h(t)=- 16t^{2}+56t$ is a quadratic function in the form $y = ax^{2}+bx + c$ where $a=-16$, $b = 56$, $c = 0$.

Step2: Use the vertex - time formula

For a quadratic function $y=ax^{2}+bx + c$, the $x$ - coordinate (in our case $t$ - coordinate for the vertex of the parabola representing the height - time relationship) of the vertex is given by $t=-\frac{b}{2a}$.

Step3: Substitute values

Substitute $a=-16$ and $b = 56$ into $t =-\frac{b}{2a}$. So $t=-\frac{56}{2\times(-16)}=\frac{56}{32}=\frac{7}{4}$.