Rocket's Max Height: Solving for ymax

In summary, a rocket initially at rest on the ground accelerates straight upward with a constant acceleration of 53.9 m/s^2 for 7.00 seconds before running out of fuel. After that, it is in free fall with a constant acceleration due to gravity of 9.80 m/s^2. To find the maximum height reached by the rocket, one must calculate the velocity after 7 seconds and then use the constant acceleration formula to determine the height at which the rocket has a velocity of 0.
  • #1
Turtlie
6
0

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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  • #2
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.
 

FAQ: Rocket's Max Height: Solving for ymax

What is "Rocket's Max Height: Solving for ymax"?

"Rocket's Max Height: Solving for ymax" is a mathematical equation used to calculate the maximum height that a rocket will reach during its flight. It takes into account variables such as the initial velocity, acceleration due to gravity, and the time of flight.

Why is it important to calculate the maximum height of a rocket?

Calculating the maximum height of a rocket allows scientists and engineers to understand the performance and capabilities of the rocket. It also helps in determining the trajectory and flight path of the rocket.

What are the key variables in the "Rocket's Max Height: Solving for ymax" equation?

The key variables in this equation are the initial velocity, acceleration due to gravity, and the time of flight. These variables can be measured or calculated using other equations.

Can the "Rocket's Max Height: Solving for ymax" equation be used for all types of rockets?

Yes, this equation can be used for all types of rockets as long as the key variables are known. However, it may not account for factors such as air resistance or wind, which can affect the actual maximum height of the rocket.

How accurate is the "Rocket's Max Height: Solving for ymax" equation?

The accuracy of this equation depends on the accuracy of the input variables and the assumptions made. It is a simplified model and may not account for all variables that can affect the maximum height of a rocket.

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