Question

Please check!!!

Answer 1

A rocket is on the ground getting ready to launch. Tim ignites the rocket, and it takes off into the air. Assume that the height of the rocket can be
modeled as a quadratic function with respect to time. It reaches a maximum height of 124 feet and lands on the ground 15 seconds after reaching the maximum height. How long was the rocket in the air?

a.) 124 seconds
b.) 60 seconds
c.) 30 seconds <----
d.) 15 seconds

Answer 2

\[h=aT ^{2} +bT +c\]
differntiate both sides wit respect to time and in LHS you will get rate of change of height of the rocket.
\[v=2aT +b\] (v is the rate of change of height )

now u know that at highest point the velocity (v) is zero. using this info u can get T = -b/2a

but you know that this T that is equal to -b/2a equals 15 sec. from here u get relation between a and b.

Answer 3

and put it in first equation.

Answer 4

To me, you are correct.