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)?

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

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).

To find the time it takes for the rocket to hit the ground, we need to solve the equation h = -16t^2 + 144t for t when h is 0.

Setting h to 0, we have:

0 = -16t^2 + 144t

To solve this equation, we can factor out a common term:

0 = 16t(9 - t)

Now, we can set each factor equal to zero and solve for t:

1) 16t = 0
t = 0

2) 9 - t = 0
t = 9

Therefore, the rocket will hit the ground when t is equal to either 0 or 9. So, it will take 9 seconds for the rocket to hit the ground.

To find the time it takes for the rocket to hit the ground, we need to set the height equation equal to zero and solve for t.

Given the equation h = -16t^2 + 144t, we substitute 0 for h, yielding:

0 = -16t^2 + 144t

Now, we can solve this quadratic equation for t.

First, divide the entire equation by -16 to simplify it:

0 = t^2 - 9t

Now, we can factor the equation:

0 = t(t - 9)

Setting each factor equal to zero, we have two possibilities:

t = 0 or t - 9 = 0

Solving for t in both cases:

1. t = 0
This solution indicates the initial time when the rocket was launched. However, we want to find the time when the rocket hits the ground, which is at h = 0 after it has been launched. Therefore, we ignore this solution.

2. t - 9 = 0
Solving for t:
t = 9

Therefore, it takes 9 seconds for the rocket to hit the ground.