How long is the rocket in the air?

Answer in units of s

Incomplete.

To determine the duration of time that the rocket is in the air, you would need to know the initial velocity (V₀) and the vertical distance (d) traveled by the rocket. Without specific values for these parameters, it is not possible to provide an exact answer. However, I can explain the steps to calculate the duration of time using the basic principles of kinematics.

1. Assuming the rocket is launched vertically upward, the initial velocity (V₀) would be positive.
2. The vertical distance traveled (d) would be the maximum height reached by the rocket.
3. Use the kinematic equation that relates the vertical displacement (d), initial velocity (V₀), time (t), and acceleration due to gravity (g):
d = V₀*t + (1/2)*g*t²
In this equation, g is usually taken as -9.8 m/s² (acceleration due to gravity).
4. Rearrange the equation to solve for time (t):
(1/2)*g*t² + V₀*t - d = 0
5. This is a quadratic equation in the form of ax² + bx + c = 0, where a = (1/2)*g, b = V₀, and c = -d.
6. Using the quadratic formula, t can be determined as:
t = (-b ± √(b² - 4ac)) / (2a)

By substituting the actual values of V₀ and d into the equation and solving for t, you can calculate the time duration in seconds (s) for which the rocket is in the air.