What is the maximum height of the rocket?

In summary, a rocket with a body mass of 0.49kg and 1.47kg of fuel, burning at a rate of 0.49kg/s with an exhaust speed of 60m/s, starts from rest. Using the equation for ln(x) and determining the thrust of the engine, the mass of the rocket+propellant with respect to time can be found. This allows for an expression for the acceleration of the rocket with respect to time, including gravitational acceleration. After the fuel runs out, the rocket becomes a simple projectile.
  • #1
demenius
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Homework Statement


A rocket has a body which consists of 0.49kg of material. This body holds 1.47kg of fuel. The fuel is consumed at a rate of 0.49kg/s, and the exhaust speed of the fuel is 60m/s. Assuming that the rocket starts from rest, what is the maximum height the rocket reaches?


Homework Equations


Note: ∫ln(x)dx = xln(x) - x


The Attempt at a Solution


None. Don't know where to start.
 
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  • #2
Start by determining the thrust (force) that the engine produces as it burns fuel at the given rate with the given exhaust speed. Then find an expression for the mass of the rocket+propellant with respect to time. With these you can write an expression for the acceleration of the rocket w.r.t. time (remember to include gravitational acceleration). With the acceleration function you can find velocity and distance with some calculus.

The rocket will have some height and speed when the fuel runs out, so it becomes a simple projectile after that.
 

1. What factors affect the maximum height of a rocket?

The maximum height of a rocket is affected by several factors, including the amount of thrust produced by the rocket's engine, the weight of the rocket, the aerodynamics of the rocket's design, and the air resistance encountered during flight.

2. How can the maximum height of a rocket be calculated?

The maximum height of a rocket can be calculated using the rocket equation, which takes into account the mass of the rocket, the mass of the propellant, and the specific impulse of the rocket's engine. Other factors such as air resistance and gravity can also be included in more complex calculations.

3. What is the maximum height that a rocket can reach?

The maximum height that a rocket can reach is determined by the specific design and capabilities of the rocket, as well as external factors such as atmospheric conditions and the presence of gravity. With current technology, rockets have been able to reach heights of over 100 miles.

4. Can the maximum height of a rocket be increased?

Yes, the maximum height of a rocket can be increased through various means such as increasing the thrust of the engine, reducing the weight of the rocket, or improving the aerodynamics of the rocket's design. However, there are limits to how high a rocket can go due to physical and technological constraints.

5. What is the maximum height that a rocket has reached?

The maximum height that a rocket has reached depends on the specific rocket and its purpose. For example, the Saturn V rocket used in the Apollo missions reached a maximum height of over 240,000 miles when sending astronauts to the moon, while other rockets have reached heights of over 100 miles when launching satellites into orbit.

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