Rocket's Max Altitude & Flight Time

In summary, a 200kg weather rocket with 100kg of fuel is fired straight up with an acceleration of 31.0 m/s^2 for 35.0 seconds before running out of fuel. The weight of the rocket is not relevant to the problem as it is set up to ignore air resistance effects. The rocket's maximum altitude and time in the air can be found by breaking the problem into two parts: when the fuel is burning and after it runs out. The height at which the fuel runs out can be determined using basic kinematics equations.
  • #1
jelder
3
0
A 200kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 31.0 {\rm m/s^2} for 35.0 s, then runs out of fuel. Ignore any air resistance effects.

I just don't know how to integrate the weight into the problem

known variables (hopefully they are correct this may be where I went wrong)
vi=0m/s
xi=0km
xf=?
a=31.0m/s^2
t=35.0s



What is the rocket's maximum altitude?



How long is the rocket in the air?
 
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  • #2
Why do you think you need to take the mass into account? I don't think that it's relevant to the question as it makes it much more complicated than just basic kinematics. Actually, the information in the question is set up so you don't have to worry about it.

Think about this question in two pieces: one piece is when the fuel is burning, and the other is after the fuel runs out.

How do you think you can find the height of the rocket at the point where the fuel just runs out?
 
  • #3


To calculate the maximum altitude and flight time of the rocket, we can use the equations of motion for constant acceleration.

First, we can use the equation xf = xi + vit + 1/2at^2 to find the final position (xf) of the rocket. Since the initial position (xi) is 0 and the initial velocity (vi) is also 0, the equation simplifies to xf = 1/2at^2. Plugging in the values, we get xf = 1/2(31.0)(35.0)^2 = 1/2(31.0)(1225) = 19037.5m. This is the maximum altitude of the rocket.

Next, we can use the equation vf = vi + at to find the final velocity (vf) of the rocket at the end of the 35.0 seconds. Again, since the initial velocity is 0, the equation simplifies to vf = at. Plugging in the values, we get vf = (31.0)(35.0) = 1085m/s. This is the maximum velocity of the rocket.

To find the flight time, we can use the equation t = vf/a. Plugging in the values, we get t = (1085)/31.0 = 35.0s. This is the total flight time of the rocket.

In order to incorporate the weight of the rocket into the problem, we can use the equation F = ma, where F is the net force, m is the mass, and a is the acceleration. The weight of the rocket can be calculated by multiplying the mass (200kg) by the acceleration due to gravity (9.8m/s^2). This gives a weight of 1960N. We can then subtract this weight from the net force to find the acceleration of the rocket due to the thrust of the fuel. This would give us a slightly different value for the acceleration (since the weight would decrease as the fuel is burned), but the overall calculations and results would be similar.

In summary, the maximum altitude of the rocket is 19037.5m, and the flight time is 35.0s. Incorporating the weight of the rocket into the problem would slightly alter the calculations, but the overall results would remain similar.
 

What factors affect a rocket's maximum altitude?

Several factors can affect a rocket's maximum altitude, including the rocket's design and construction, the amount and type of fuel used, the weight of the payload, and any external forces such as wind or air resistance.

How is a rocket's maximum altitude calculated?

A rocket's maximum altitude is typically calculated using mathematical equations that take into account the rocket's thrust, mass, and drag, as well as the gravitational pull and atmospheric conditions of the launch site.

What is the typical flight time of a rocket?

The flight time of a rocket can vary greatly depending on its design and purpose. A small hobby rocket may only have a flight time of a few seconds, while a larger rocket designed for space travel can have a flight time of several minutes or even hours.

How do engineers increase a rocket's maximum altitude?

To increase a rocket's maximum altitude, engineers may make modifications to its design and construction to reduce weight and improve aerodynamics. They may also use more powerful engines or optimize the fuel mixture to increase thrust.

What is the record for the highest rocket flight altitude?

The record for the highest rocket flight altitude is currently held by NASA's Juno spacecraft, which reached an altitude of 1.2 billion kilometers during its mission to Jupiter. This is equivalent to roughly 0.0002% of the distance from Earth to the sun.

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