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.