A rocket is shot into the air with an initial velocity of 800m/sec. The equation h = -16t2+144t models the height of the ball. how long does it take for the rocket to hit the ground (h=0)?

Answer 1

Set h to 0:
0 = -16t2 + 144t
Factor to find the t-intercepts. These are the times when the height is 0 ( i.e. when rocket is on ground).

Answer 2

Your given equation does not match your given data.
If the initial velocity is 800 m/sec, then the equation would be

h = -16t^2 + 800t , when shot from ground level.

follow "Nonetheless' " suggestion and find the x-intercept

0 = 16t^2 + 800t
16t(t - 50) = 0

take over