# Speed of a bullet

1. Feb 22, 2016

### reminiscent

1. The problem statement, all variables and given/known data
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?

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

3. 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.

Last edited: Feb 22, 2016
2. Feb 22, 2016

### ehild

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. Feb 22, 2016

### reminiscent

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. Feb 22, 2016

### ehild

After the bullet leaves the gun, there is no force the gun can exert on it.

5. Feb 22, 2016

### reminiscent

So gravity is the only force exerting on the bullet, correct?

6. Feb 22, 2016

### ehild

Yes. You do not need to bother with the stage when the bullet is inside the gun.

7. Feb 22, 2016

### reminiscent

So for part b), I should be able to use a kinematics equation, but acceleration would be 9.81 m/s^2, correct?

8. Feb 22, 2016

### ehild

The gun moves upward, but the acceleration is downward. You need to take this into account in the sign of the acceleration.

9. Feb 22, 2016

### reminiscent

Sorry, I meant -9.81 m/s^2. Thank you!

10. Feb 22, 2016

### ehild

You are welcome.