Finding muzzle velocity using range and height of barrel

In summary, the conversation is about a physics assignment involving building an air cannon and determining the muzzle velocity. The equations and variables needed for this task are provided. The main goal is to rearrange the equations to solve for muzzle velocity and implement them in a spreadsheet.
  • #1
physicsisrad
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Homework Statement


Ok, so pretty much, I built an air cannon for my physics assignment. I need to determine the muzzle velocity. I know the angle of the barrel, the height of the muzzle about the ground and the distance the projectile covered. I fired projectile at multiple pressures in order to determine the effect of pressure of muzzle velocity. I am ignoring drag and friction for these equations.

Homework Equations


Let v0 = Initial muzzle velocity
o = angle of barrel = (33.82 Degrees if this is neccessarY)
Height of barrel = h = 1.13m

The Attempt at a Solution


Total time of flight= t = v0sin(o)/9.8^2+ (v0sin(o)^2/9.8^2 - 2*h/9.8)^0.5
Distance traveled = v0cos(o) * t
= v0cos(o) * (v0sin(o)/9.8^2+ (v0sin(o)^2/9.8^2 - 2*h/9.8)^0.5)
I need the rearrange this equation so v0 is the subject so I can implement this in an excel spreadsheet as I have literally hundreds of these to determine.

 
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  • #2
What is your question?

If you are trying to find muzzle velocity, you have to solve these equations for time:

(1) [tex]x = v_0\cos\theta t[/tex]

(2) [tex]y = v_0\sin\theta t - \frac{1}{2}gt^2[/tex]

Find the muzzle velocity by substituting t into (1).

AM
 
Last edited:

1. What is the formula for finding muzzle velocity using range and height of barrel?

The formula for finding muzzle velocity using range and height of barrel is: v = √(g * h * tan(theta)) * √(2 * range * cos(theta)), where v is the muzzle velocity, g is the acceleration due to gravity, h is the height of the barrel, theta is the angle of elevation, and range is the distance to the target.

2. What is the significance of finding muzzle velocity using range and height of barrel?

Finding muzzle velocity using range and height of barrel allows scientists and engineers to accurately measure the initial velocity of a projectile fired from a gun. This information is crucial in fields such as ballistics, military defense, and sports.

3. How do you measure the height of a barrel for calculating muzzle velocity?

The height of the barrel can be measured by using a ruler or measuring tape to determine the distance between the ground and the center of the barrel's opening. It is important to measure from the center of the opening to account for any variations in the barrel's position.

4. Can muzzle velocity be calculated without knowing the exact range to the target?

No, the range to the target is a crucial component in the formula for finding muzzle velocity. Without knowing the range, the calculation would be inaccurate.

5. How does the angle of elevation affect the calculation of muzzle velocity?

The angle of elevation is a key factor in determining the muzzle velocity. A higher angle of elevation will result in a higher muzzle velocity, while a lower angle of elevation will result in a lower muzzle velocity. This is because the angle of elevation affects the horizontal and vertical components of the projectile's velocity.

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