Finding max height and speed before it hits the ground of a rocket

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SUMMARY

The discussion focuses on calculating the maximum height and speed of a model rocket fired vertically upward with a constant acceleration of 40 m/s² for 2.5 seconds before entering free fall. The maximum height reached by the rocket is determined to be 635 meters, while the speed just before it impacts the ground is calculated to be 112 m/s. The effects of gravity are included in the calculations, which utilize kinematic equations to derive these results.

PREREQUISITES
  • Kinematic equations for uniformly accelerated motion
  • Understanding of free fall dynamics
  • Basic principles of physics related to projectile motion
  • Knowledge of acceleration due to gravity (9.81 m/s²)
NEXT STEPS
  • Study the derivation of kinematic equations for vertical motion
  • Learn about the effects of air resistance on projectile motion
  • Explore advanced topics in rocket propulsion and thrust
  • Investigate the principles of energy conservation in free fall
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Students studying physics, educators teaching kinematics, and hobbyists interested in model rocketry and motion analysis.

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Homework Statement



A model rocket initially at rest on the ground is fired vertically upward, and the engine thrust produces a constant acceleration a = 40 m/s2. After running for 2.5 s the engine is cut off and then the rocket is in free fall. (a) Find the maximum height that the rocket reaches. (b) Find the speed of the rocket just before it hits the ground.
Ans: (b) 635 m (c) 112 m/s
Note: The rocket travels with 40 m/s2 acceleration during the first 2.5 s (gravity effect included).


Homework Equations





The Attempt at a Solution

 
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In the relevant equations, can you write the kinematic equations. And using the given data, you can select a proper equation to solve the problem.
 

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