If a rocket is launched with an initial velocity of 1600 feet per second when will the rocket be 14400 feet high?

i want the ANSWER!!!!!!!!!!!!

the answer is 10 and 90 seconds

h=vi*t-32t^2

solve for t

To find out when the rocket will be 14400 feet high, we need to determine the time it takes for the rocket to reach that height. We'll use the kinematic equation for projectile motion to solve this problem.

The equation we'll use is:

h(t) = h0 + v0*t - (1/2)*g*t^2

where:
h(t) is the height at time t,
h0 is the initial height,
v0 is the initial velocity,
g is the acceleration due to gravity, and
t is the time.

In this case, the initial height is 0 (since the rocket is launched from the ground), the initial velocity is 1600 feet per second, and g is approximately 32 feet per second squared.

Plugging in these values, we get:

14400 = 0 + 1600*t - (1/2)*32*t^2

Simplifying the equation, we have:

0 = 32*t^2 - 1600*t + 14400

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring may not be easy, so we'll use the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / (2a)

For our equation, a = 32, b = -1600, and c = 14400. Plugging in these values, we get:

t = (-(-1600) ± sqrt((-1600)^2 - 4*32*14400)) / (2*32)

Simplifying further:

t = (1600 ± sqrt(2560000 - 1843200)) / 64

t = (1600 ± sqrt(716800)) / 64

Now, let's calculate the values:

t = (1600 ± 848.53) / 64

This gives us two possible values for t:

t₁ = (1600 + 848.53) / 64 ≈ 37.885 seconds
t₂ = (1600 - 848.53) / 64 ≈ 13.678 seconds

So, the rocket will be 14400 feet high approximately 13.678 seconds and 37.885 seconds after it is launched.