Find velocity with projectile and recoil accelerations

In summary, the conversation is discussing a problem involving a rolling projectile launcher that is initially at rest. Compressed air accelerates the projectile through a distance of 2.00 m in a pipe, with an acceleration of 36.0 m/s^2 with respect to the pipe, and a recoil acceleration of 15.0 m/s^2 with respect to the ground. The goal is to calculate the velocity of the projectile as it leaves the pipe, using the given data. Suggestions for solving the problem include using constant acceleration equations and considering the height difference and time it takes to reach the top of the barrel.
  • #1
PAstudent
47
0

Homework Statement



A rolling projectile launcher is initially at rest. Then internal compressed air accelerates the projectile through a distance L in a pipe (see diagram). The acceleration of the projectile with respect to the pipe is ap. During the launch the launcher has a recoil acceleration ar with respect to the ground. Both accelerations are constants. Use the data given below and calculate the velocity, with respect to the ground, of the projectile as it leaves the pipe.

Data: L = 2.00 m, theta= 53.0, ap = 36.0 m/s2. ar = 15.0 m/s2

Projectile launcher.png

Homework Equations


Constant acceleration equations
[/B]

The Attempt at a Solution


I have never seen anything like this before. However, I tried setting up it up like a projectile motion problem with what I knew

Xo=0 Yo=0 because at rest then accelerations would ax= 36cos(53)-15 and ay=36sin(53)

I just wanted to put this out there and see if I am remotely near the path of solving this problem correctly[/B]
 
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  • #2
PAstudent said:
Xo=0 Yo=0 because at rest then accelerations would ax= 36cos(53)-15 and ay=36sin(53)
That is a possible approach I guess. You know the vertical acceleration, and you can calculate the height difference the projectile covers in the barrel. That should help to find more parameters.
 
  • #3
Are you saying vertical acceleration as the acceleration due to gravity?
 
  • #4
Any body have any more guidance or hints?
 
  • #5
Ignore gravity. The origin of the acceleration is not relevant here.

How much is the top of the barrel above the bottom?
You accelerate an object vertically with acceleration ay. How long does it take to reach this height?
PAstudent said:
Any body have any more guidance or hints?
I didn't forget the thread, but if you don't get answers between 1 AM and 2 AM (central European time) it is not hard to guess why. No reason to add such a post.
 

FAQ: Find velocity with projectile and recoil accelerations

1. How do you calculate the velocity of a projectile using acceleration?

The velocity of a projectile can be calculated using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. The acceleration can be broken down into its horizontal and vertical components, and the velocity can be calculated separately for each component.

2. What is the difference between projectile acceleration and recoil acceleration?

Projectile acceleration refers to the acceleration of an object that is moving through the air due to the force of gravity. Recoil acceleration, on the other hand, refers to the acceleration of a firearm or other weapon as a result of the force exerted on it by the projectile being fired.

3. Can projectile and recoil accelerations be calculated simultaneously?

Yes, projectile and recoil accelerations can be calculated simultaneously by taking into account the forces acting on the projectile and the firearm. This can be done using equations such as Newton's second law of motion, which states that the sum of all forces acting on an object is equal to its mass multiplied by its acceleration.

4. How does air resistance affect the velocity of a projectile?

Air resistance, also known as drag, can slow down the velocity of a projectile by exerting a force in the opposite direction to its motion. This force increases as the velocity of the projectile increases, resulting in a decrease in acceleration. In order to accurately calculate the velocity of a projectile taking into account air resistance, complex mathematical models and equations must be used.

5. Are there any real-life applications for calculating velocity with projectile and recoil accelerations?

Yes, there are many real-life applications for calculating velocity using projectile and recoil accelerations. This can be useful in fields such as ballistics, where the velocity of a bullet or other projectile is crucial in determining its trajectory and impact. It is also important in the design and testing of firearms and other weapons, as well as in sports such as archery and javelin throwing.

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