H(t)=-t^2+12t+5

Question

what is the intail height of the rocket ?

Find the height of the rocket above the ground after 7 seconds.?

After how many seconds does it take for the rocket to be at its maximum?

Find the maximum height of the rocket above ground

When does the rocket hit the ground(round answer to 3 significant figuers)

Answer 1

initial height = 5

h(t) =-t^2 +12t + 5. take the derivative, set =0, solve for t

h'(t) =-2t +12 = 0, t=12/2 = 6 seconds to reach max height

h(6) = -6^2 +12(6) +5 = 41 feet= max height

h(7) = -7^2 +12(7) + 5 = 40 feet = height after 7 seconds