"5000kg Interceptor Rocket Trajectory & Speed

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Homework Help Overview

The discussion revolves around the trajectory and speed of a 5000kg interceptor rocket launched at an angle, with specific focus on deriving an equation for its trajectory, understanding the shape of that trajectory, and determining the elevation at which it reaches the speed of sound.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the initial launch angle and question whether it should be adjusted. There is mention of the initial velocity being zero and the impact of gravity on the trajectory. Some participants suggest writing equations for vertical and horizontal motion to analyze the situation further. Others express uncertainty about starting the calculations due to the initial velocity being zero.

Discussion Status

The discussion is active, with participants exploring various interpretations of the problem. Some have provided insights into the nature of the trajectory and the effects of gravity, while others are seeking hints to progress further. There is acknowledgment of the complexity involved, particularly regarding differential equations and varying acceleration.

Contextual Notes

Participants note that the problem sheet may contain a hint regarding the launch angle, and there is a concern about the implications of an initial velocity of zero on the calculations. The discussion also reflects on the limitations of analytical methods compared to computer simulations.

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Homework Statement


A 5000kg interceptor rocket is launched at an angle of 44.7 degrees. The thrust of the rocket motor is 140,700N
a) Find an equation y(x) that describes the rocket's trajectory
b) What shape is the trajectory?
c) At what elevation does the rocket reach the speed of sound, 330m/s?

Homework Equations


kinematic equations
Newton's laws


The Attempt at a Solution


The problem sheet hint tells me that the angle is not 44.7 degrees. So is it right that it should be 45.3 degrees then? Furthermore, speed initial is 0m/s correct?
 
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The angle will vary. The force of gravity will reduce the angle. It will be a curved trajectory with the angle continuously changing. Yes, it appears that the initial velocity is zero.

Write the equations for vertical and horizontal motion to find out what happens. Looks interesting!
 
Delphi51 said:
The angle will vary. The force of gravity will reduce the angle. It will be a curved trajectory with the angle continuously changing. Yes, it appears that the initial velocity is zero.

Write the equations for vertical and horizontal motion to find out what happens. Looks interesting!

I don't see how to start off a then because I get something over the initial velocity squared, which is zero. As a result, it should not be defined. Any hints?
 
Oops, sorry, I shouldn't have commented. I don't know how to solve it. Quite a little set of differential equations involved! I can find the answers using a computer simulation but I've lost the ability to do varying acceleration problems via calculus.

Funny, according to my little spreadsheet model, it doesn't get far off the ground.
The component of the thrust in the vertical direction is very soon overcome by gravity and the rocket loses angle very quickly.
rocket.jpg
 
Last edited:

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