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

In summary: So for part b), I should be able to use a kinematics equation, but acceleration would be 9.81 m/s^2,...When the bullet leaves the gun, it has a speed of 40 m/s and it will reach a maximum height of 50 m. When flying in the air, its velocity decreases to 40 m/s at high of 50 m.
  • #1
reminiscent
131
2

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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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?
 
  • #6
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.
 
  • #7
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?
 
  • #8
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.
 
  • #9
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.
 

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

What is the average speed of a bullet fired from a hunter's rifle?

The average speed of a bullet fired from a hunter's rifle can vary depending on the specific rifle and ammunition used, but it is typically around 2,500 feet per second.

How does the speed of a bullet affect its accuracy?

The speed of a bullet can greatly impact its accuracy. A faster bullet will have less time to be affected by external factors such as wind, resulting in more accurate shots. However, if the bullet is too fast, it may be more difficult to control and can cause damage to the barrel of the rifle.

What factors can affect the speed of a bullet?

The speed of a bullet can be affected by various factors, including the type and quality of the rifle, the type and weight of the bullet, the amount and type of gunpowder used, and external factors such as wind and temperature.

How does the speed of a bullet impact its trajectory?

The speed of a bullet has a significant impact on its trajectory. A faster bullet will experience less drop over distance and will also have a flatter trajectory, making it easier to hit a target at longer ranges.

How does the speed of a bullet fired at a duck in flight affect the likelihood of a successful hit?

The speed of a bullet fired at a duck in flight is crucial for a successful hit. The bullet must be traveling at a high enough speed to reach the duck before it can move out of the way. Too slow of a bullet can result in a miss, while too fast of a bullet can cause the duck to disintegrate, making it difficult to retrieve for consumption.

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