Range of a Rocket Launched from Height h

In summary, The method for finding the range of a rocket launched from height h given three forces (weight, drag, and thrust) is to solve for each axis independently and then measure the time it takes for the rocket to move on the y-axis. This time is then used to calculate the range, which is equal to the horizontal position x at time T. However, this method may not work if only the height h is given, as it requires two inputs (initial position and initial velocity) to solve a 2nd order Differential equation.
  • #1
quarkon
1
0
hello guys
could anybody tell me the method of finding the range of a rocket launched from height h,
the rocket of course is under three forces weight,drag and thrust
 
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  • #2
well I don't know the answer since you want to put drag and thrust in the game...
But for one thing I'm sure about- with your input nobody will be able to answer your question... why?
Because whatever you do, the equation you'll have to solve will be a 2nd order Differential equation, so you need 2 inputs (initial position and initial velocity). So giving just the height [itex]h[/itex] you can't get an answer :P
 
  • #3
the method though is easy-
x-y axis: x is the horizontal, y the vertical... in each axis the movement of the rocket is independent (i think this is also true for the extra thrust and drag forces). So you solve for each independently. Then you measure how long it will move on the y axis, and put that time in the x(t) you'll have obtained. Let's say that time t=T... then the range will be R=x(T)
 

FAQ: Range of a Rocket Launched from Height h

What is the range of a rocket launched from height h?

The range of a rocket launched from height h is the horizontal distance it travels from the point of launch until it reaches the ground. It is affected by a number of factors such as the initial velocity, air resistance, and the height of launch.

How is the range of a rocket calculated?

The range of a rocket can be calculated using the following formula:
R = (V^2 * sin(2θ)) / g
where R is the range, V is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

What is the optimal angle of launch for maximum range?

The optimal angle of launch for maximum range is 45 degrees. This angle allows for the greatest horizontal distance while still maintaining a significant vertical height, allowing the rocket to stay in the air for a longer period of time.

How does air resistance affect the range of a rocket?

Air resistance can significantly decrease the range of a rocket. As the rocket travels through the air, it experiences drag force which opposes its motion. This reduces its horizontal velocity and ultimately results in a shorter range.

Can the range of a rocket be increased by launching it from a higher height?

Yes, launching a rocket from a higher height can increase its range. This is because the higher initial height provides the rocket with more potential energy, which can be converted into kinetic energy and increase its horizontal velocity. However, this effect is limited and other factors such as air resistance and initial velocity also play a role in determining the range.

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