# Determine the launching speed of the object

• Kryptix
In summary, this person is studying engineering and has a problem determining the trajectory of an object being launched from a nozzle. They are trying to use conservation of momentum to calculate the velocity, but are not sure of the mass of the air. They have a sketch of the setup, but need more information to complete the calculation.
Kryptix
So this is probably a very basic question. I'm studying EE so this is kind of out of my field as i have never taken this but I'm working on a project and it involves a pressurized container releasing air into a tube and launching something out the nozzle.

The problem I'm having is that I'm not entire sure how to determine the launching speed of the object given purely the velocity of the air exit the nozzle.

I've been doing research and some calculations that at ~54psia the air exiting the nozzle would be moving at mach 1 speeds (~300m/s) as long at the ratio between p/po is less than 0.528

I've been thinking of using the basic principle of conservation of momentum in order to determine the launching velocity of the solid leaving the nozzle, but I run into a problem. I'm not sure of the mass of air.

I've asked around as well and people have mentioned things such as control volume but have provided no explanation as to what it is or how to set it,(not to mention how to use it).

Any help on determining the exit velocity of a solid given the velocity of the air would be greatly appreciated.

Thanks again :)
Other info: Diameter of Nozzle: 0.5 inch. PSI: 40. Atmospheric pressure: 1atm
Mass of solid being launched: 7 grams.

Do you have a sketch of the setup? In the limit of long nozzles, the mass will approximately reach the same speed as air without the projectile. For very short nozzles, speed is limited by the acceleration given by the pressure difference. Everything between is more complicated.

mfb said:
Do you have a sketch of the setup? In the limit of long nozzles, the mass will approximately reach the same speed as air without the projectile. For very short nozzles, speed is limited by the acceleration given by the pressure difference. Everything between is more complicated.
umm yeah, i have the sketch but i'd have to wait til i get home to get. For now I can tell you that the travel path of the air and the solid is about 2 ft.

I will post sketch later.

## 1. What is the equation for determining the launching speed of an object?

The equation for determining the launching speed of an object is v = √(2gh), where v is the launching speed, g is the acceleration due to gravity (9.8 m/s²), and h is the height from which the object is launched.

## 2. How do you measure the height from which the object is launched?

The height can be measured using a ruler or measuring tape. If the launch is on an incline, the height can be determined by using trigonometry to calculate the vertical component of the launch angle.

## 3. Can the launching speed of an object be greater than the speed of light?

No, according to the theory of relativity, the speed of light (299,792,458 m/s) is the maximum speed that any object can attain. Therefore, the launching speed of an object cannot exceed the speed of light.

## 4. What factors can affect the accuracy of the calculated launching speed?

The accuracy of the calculated launching speed can be affected by factors such as air resistance, wind, and human error in measuring the height or timing the launch. The launch surface and launch angle can also affect the speed.

## 5. Can the launching speed of an object be determined without knowing the height of the launch?

No, the height of the launch is a crucial component in the equation for determining launching speed. Without knowing the height, the speed cannot be accurately calculated.

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