Solution:
Given that;
A rocket is launched (from the ground) with an initial upward velocity of 256 feet per second.
To find how long it will take, the formula for the height in feet per second is
[tex]h(t)=-16t^2+v_0t+h_0[/tex]
Where
[tex]\begin{gathered} h_0\text{ is the initial height} \\ v_0\text{ is the initial velocity} \\ t\text{ is the time taken} \\ h\text{ represent the height} \end{gathered}[/tex]
Since, the rocket was launch from the ground and the rocket will return to the ground,
[tex]\begin{gathered} h(t)=0 \\ h_0=0 \\ v_0=256 \end{gathered}[/tex]
Substitute the values of the variables into the formula above
[tex]\begin{gathered} h(t)=-16t^{2}+v_{0}t+h_{0} \\ 0=-16t^2+256t+0 \\ -16t^2+256t=0 \end{gathered}[/tex]
The equation is
[tex]-16t^2+256t=0[/tex]
Solving the quadratic equation
[tex]\begin{gathered} 16t^2-256t=0 \\ 16t(t-16)=0 \\ 16t=0 \\ t=0 \\ t-16=0 \\ t=16 \\ t=0\text{ or 16} \end{gathered}[/tex]
The time taken for the rocket to take off will be t = 0,
Hence, it will take 16 seconds for the rocket to return to the ground.
