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To find the interval during which the rocket’s height \( h \) is increasing, we need to analyze the given graph of height \( h \) (in feet) as a function of time \( t \) (in seconds).

From the graph, it is clear that:
- The height increases from \( t = 0 \) seconds up to the peak at \( t = 25 \) seconds, where the rocket reaches its maximum height of 10,000 feet.
- After reaching this peak, the height starts to decrease until it reaches the ground again at \( t = 50 \) seconds.

Therefore, the interval during which the rocket's height is increasing is:
\[
0 < t < 25
\]

This interval indicates that from launch until it reaches its maximum height, the rocket's height is increasing.

Would you like more details on this solution, or have any other questions?

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Here are 5 related questions for further exploration:
1. What is the interval where the rocket's height is decreasing?
2. How would you determine the maximum height using calculus if only the equation of height as a function of time were given?
3. What is the average speed of the rocket on its ascent to the maximum height?
4. How long does it take for the rocket to return to the ground after reaching its peak?
5. How would air resistance affect the rocket’s trajectory?

**Tip:** In physics problems involving projectile motion, the time to reach the maximum height is typically half the total time if the projectile lands at the same level as its launch point.

A rocket is launched in the air. The graph below shows the height of the rocket h in feet after t seconds. Find the interval for which the rocket’s height is increasing.

Learn how to determine the interval during which a rocket's height is increasing using graph interpretation. This problem involves identifying intervals from a height-time graph and is suitable for students in Grades 8-10.

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