Answer:
[tex]h(t)=-16t^{2}+120t+2[/tex]
Step-by-step explanation:
we know that
The height of Justin’s rocket is modeled by the equation
[tex]h(t)=-16t^{2}+60t+2[/tex]
This is the equation of a vertical parabola open downward
The vertex is a maximum
where
The coefficient of t^2 represent the acceleration
[tex]a=-16[/tex]
The coefficient of t represent the initial velocity
[tex]v=60[/tex]
The constant of the equation represent the initial height
[tex]h_0=2[/tex]
Remember that
Elena launched his rocket from the same position, but with an initial velocity double that of Justin’s
so
Now the initial velocity is
[tex]v=60(2)=120[/tex]
substitute
The height of Elena’s rocket is the equation
[tex]h(t)=-16t^{2}+120t+2[/tex]
