Rocket's Max Height: Solving for ymax

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SUMMARY

The maximum height (ymax) reached by a rocket with a constant upward acceleration of 53.9 m/s² for 7 seconds is calculated to be 2,641 meters. After the fuel is exhausted, the rocket continues to ascend until its velocity reaches zero due to the influence of gravity (9.80 m/s²). To determine the additional height gained during free fall, one must first calculate the velocity at the end of the propulsion phase and then apply kinematic equations to find the height at which the rocket stops ascending.

PREREQUISITES
  • Understanding of kinematic equations for uniformly accelerated motion
  • Knowledge of free fall dynamics under gravitational acceleration
  • Familiarity with the concepts of initial velocity and final velocity
  • Basic algebra for solving equations
NEXT STEPS
  • Calculate the final velocity of the rocket after 7 seconds of acceleration using the formula v = u + at
  • Apply the kinematic equation to determine the additional height gained during free fall: h = v² / (2g)
  • Explore the implications of air resistance on rocket motion for more advanced scenarios
  • Investigate the effects of varying acceleration profiles on maximum height calculations
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and kinematics, as well as educators seeking to enhance their teaching of motion under gravity.

Turtlie
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Homework Statement


A rocket, initially at rest on the ground, accelerates straight upward from rest with constant acceleration 53.9 m/s^2. The acceleration period lasts for time 7.00 s until the fuel is exhausted. After that, the rocket is in free fall.

Find the maximum height ymax reached by the rocket. Ignore air resistance and assume a constant acceleration due to gravity equal to 9.80 m/s^2 .

The Attempt at a Solution


I got 2,641m, but it says that the rocket will still be moving upwards after the fuel is lost. How would I find how far the rocket goes after it runs out of fuel?
 
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From the moment the fuel finishes, only one force acts upon the rocket: gravity.
So find the the velocity the rocket possesses after those 7 seconds of propulsion and then use the constant acceleration formulae to find the height at which the rocket has v=0.


R.
 

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