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The problem involves a rocket launched with an initial velocity and a constant acceleration, and we are asked to find the time it takes for the rocket to reach a certain height.

Given:
- Initial velocity \( u = 128 \, \text{m/s} \)
- Final velocity \( v = 200 \, \text{m/s} \)
- Displacement \( s = 180 \, \text{m} \)

We can use the following kinematic equation that relates velocity, displacement, and acceleration:

\[
v^2 = u^2 + 2as
\]

Where:
- \( v \) is the final velocity
- \( u \) is the initial velocity
- \( a \) is the acceleration
- \( s \) is the displacement

First, we'll solve for \( a \) (acceleration), then use it to find the time \( t \) using the formula:

\[
v = u + at
\]

Let's compute the acceleration and time.The acceleration of the rocket is \( 65.6 \, \text{m/s}^2 \), and the time it takes for the rocket to reach the height of 180 meters is approximately \( 1.10 \, \text{seconds} \).

Would you like more details or have any other questions?

Here are five related questions:
1. What is the total distance traveled by the rocket after 5 seconds?
2. How would the time change if the rocket had a different initial velocity?
3. What is the velocity of the rocket after 3 seconds?
4. How long would it take the rocket to reach a height of 300 meters?
5. What is the final velocity if the rocket reaches a height of 250 meters?

**Tip:** In kinematic problems, always identify which variables are known to choose the appropriate equation.

A rocket is launched with initial velocity 128 m/s and travels with constant acceleration. When the rocket has reached a height of 180 m above its launch position, its velocity is 200 m/s. How long did it take the rocket to reach this height?

Solve how long it takes a rocket to reach a height of 180 meters with initial velocity of 128 m/s and a final velocity of 200 m/s using kinematic equations. Suitable for high school and college-level physics.

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