Speed of a Bullet: Hunter's Rifle & Duck Flight

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Homework Help Overview

The problem involves a hunter's rifle aimed at a duck flying 50 m above the gun. The bullet, weighing 5 N, is shot upwards with an initial speed of 40 m/s upon hitting the duck. The questions focus on determining the bullet's speed as it leaves the rifle and the maximum height it would reach if it missed the duck. The discussion revolves around the application of work-energy principles and kinematics in analyzing the bullet's motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the applicability of kinematics versus work-energy equations, with some expressing uncertainty about the forces acting on the bullet. There are attempts to clarify the role of gravity and the forces involved during the bullet's flight. Questions arise regarding the calculation of total work and the acceleration of the bullet.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been provided regarding the forces acting on the bullet after it leaves the gun, emphasizing that gravity is the only force at play during its flight. There is recognition of the need to consider the direction of acceleration when applying kinematic equations.

Contextual Notes

Participants note that the bullet's acceleration while inside the gun is not necessary for solving the problem, and there is a focus on the implications of gravity as the sole force acting on the bullet after it exits the gun.

reminiscent
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Homework Statement


A hunter’s rifle is pointed upwards in a vertical position aiming at a duck flying 50 m above the gun. The bullet has a weight of 5 N and it is shot moving upward with a speed of 40 m/s when it hits the duck. (a) What is the speed of the bullet as it leaves the rifle? (b) What would be the maximum height the bullet would reach if it had missed the duck?

Homework Equations


Not sure if I have to use Work equations or kinematics equations.

The Attempt at a Solution


I pointed out knowns and unknowns so far, but I am unsure if I should use a kinematics equation (for the y-direction) - the bullet feels a force of gravity, and gravity is constant, so I can use a kinematics equation. But, the bullet is accelerating upwards, and acceleration is not constant. We are discussing Work right now so it wouldn't make sense if this whole problem was about kinematics... should I draw a FBD of the bullet and figure out the forces acting upon it? Is it a Work-Kinetic Energy problem?
Edit: I know for sure now it is not a kinematics problem. It has to be a Work-Kinetic Energy problem. The thing is, I am attempting to calculate total work done on the bullet, and there is a force on the bullet from the gun going upwards, but it is not given to us. I found the work done by gravity and it is -250 J.
 
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reminiscent said:

Homework Statement


A hunter’s rifle is pointed upwards in a vertical position aiming at a duck flying 50 m above the gun. The bullet has a weight of 5 N and it is shot moving upward with a speed of 40 m/s when it hits the duck. (a) What is the speed of the bullet as it leaves the rifle? (b) What would be the maximum height the bullet would reach if it had missed the duck?

Homework Equations


Not sure if I have to use Work equations or kinematics equations.

The Attempt at a Solution


I pointed out knowns and unknowns so far, but I am unsure if I should use a kinematics equation (for the y-direction) - the bullet feels a force of gravity, and gravity is constant, so I can use a kinematics equation. But, the bullet is accelerating upwards, and acceleration is not constant. We are discussing Work right now so it wouldn't make sense if this whole problem was about kinematics... should I draw a FBD of the bullet and figure out the forces acting upon it? Is it a Work-Kinetic Energy problem?
Edit: I know for sure now it is not a kinematics problem. It has to be a Work-Kinetic Energy problem. The thing is, I am attempting to calculate total work done on the bullet, and there is a force on the bullet from the gun going upwards, but it is not given to us. I found the work done by gravity and it is -250 J.
The bullet accelerates upwards while in the gun, and reaches some speed when leaves the gun. When flying in the air, its velocity decreases to 40 m/s at high of 50 m.
What is the acceleration of the gun when it flies ?
You can solve the problem using either kinematic equations or Work-Energy theorem.
 
ehild said:
The bullet accelerates upwards while in the gun, and reaches some speed when leaves the gun. When flying in the air, its velocity decreases to 40 m/s at high of 50 m.
What is the acceleration of the gun when it flies ?
You can solve the problem using either kinematic equations or Work-Energy theorem.
I want to use the Work-Energy theorem but I don't know how to get total work completely - isn't there a force going upwards which relates to the gun acting on the bullet? How would I be able to calculate that?
 
reminiscent said:
I want to use the Work-Energy theorem but I don't know how to get total work completely - isn't there a force going upwards which relates to the gun acting on the bullet? How would I be able to calculate that?
After the bullet leaves the gun, there is no force the gun can exert on it.
 
ehild said:
After the bullet leaves the gun, there is no force the gun can exert on it.
So gravity is the only force exerting on the bullet, correct?
 
reminiscent said:
So gravity is the only force exerting on the bullet, correct?
Yes. You do not need to bother with the stage when the bullet is inside the gun.
 
ehild said:
Yes. You do not need to bother with the stage when the bullet is inside the gun.
So for part b), I should be able to use a kinematics equation, but acceleration would be 9.81 m/s^2, correct?
 
reminiscent said:
So for part b), I should be able to use a kinematics equation, but acceleration would be 9.81 m/s^2, correct?
The gun moves upward, but the acceleration is downward. You need to take this into account in the sign of the acceleration.
 
ehild said:
The gun moves upward, but the acceleration is downward. You need to take this into account in the sign of the acceleration.
Sorry, I meant -9.81 m/s^2. Thank you!
 
  • #10
You are welcome.
 

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