A 0.5-oz model rocket is launched vertically from rest at time t=0 with a constant thrust of 0.9 lb for 0.3 s and no thrust for t> 0.3 s. Neglecting air resistance and the decrease in mass of the rocket, determine (a) the maximum height h reached by the rocket, (b) the time required to reach this maximum height.

Answer

The maximum height reached by the rocket is approximately 22.5 feet, and the time required to reach this maximum height is approximately 1.1 seconds.

Explanation

To solve this problem, we need to follow several steps. First, we convert the mass of the rocket from ounces to slugs. Then, we calculate the acceleration during the thrust period using Newton's second law. Next, we determine the velocity of the rocket at the end of the thrust period. Using this velocity, we calculate the height reached during the thrust period. Finally, we use the velocity at the end of the thrust period to find the maximum height and the time required to reach this maximum height.

Step-by-Step

1. Convert the mass of the rocket to slugs. 2. Calculate the acceleration during the thrust period. 3. Determine the velocity at the end of the thrust period. 4. Calculate the height reached during the thrust period. 5. Use the velocity at the end of the thrust period to find the maximum height. 6. Calculate the time to reach the maximum height.