When a bullet is dropped from the same height?

CBSE 11-science - Physics

Please give answer

Asked by ankurgoyal616 | 27 Sep, 2022, 03:07: PM

CBSE 11-science - Physics

please solve it sir  

Asked by satishkashyap02022004 | 29 Apr, 2020, 03:07: PM

ANSWERED BY EXPERT

CBSE 11-science - Physics

Asked by gharesaiprasad1224 | 27 Apr, 2020, 08:40: PM

ANSWERED BY EXPERT

If you didn't catch the latest MythBusters (yeah! new episodes), they did something straight from the physics textbooks. Just about every text has this example of shooting a bullet horizontally and dropping a bullet from the same height. The idea is that they should hit the ground at the same time. No one but the MythBusters could actually show this demo with a real gun.

The Physics

I am going to do some calculations, but I want to first write about the physics that accompanies this idea (and you can actually do it your self without the gun). What physics principle does this demo show? Well, it shows two things. First, it shows that the horizontal and vertical motion in projectile motion are independent. That is, what happens in the y-direction, stays in the y-direction. Really, you can treat projectile motion as two separate problems that just happen to take the same amount of time. The second thing it shows is that the velocity in one direction does not effect the velocity in the other direction (which really is the same as the first thing). Let me draw two diagrams, one for a dropped ball and one for ball shot horizontally.

There are some really important things to note in this diagram. First, the force is only in the y-direction. This means that the red ball's x-motion does not change and neither does the blue ball's. Second, the acceleration in the y-direction for both balls will be the same. Even if the balls had different masses, this would be true since a greater mass would have a greater gravitational force from the Earth.

Since the x- and y-motions are independent, and since the balls have the same y-motion they would hit the ground at the same time.

But what about air resistance?

Yes, this complicates things somewhat. First, I will use a typical model for air resistance that depends on some stuff and the speed of the object. Here is the model:

This is the magnitude of the air resistance. The direction is in the opposite direction as the way the object moves. So, here is a bullet shot horizontally from a gun with air resistance.

Here there is a difference. Now there is a component of force that depends on velocity in the y-direction. Will this make it hit the ground at a different time than one that is just dropped? Even if that one also has air resistance? Let's just do it. Of course, I am not the MythBusters. I don't even own a gun. I do own a computer.

Modeling Bullet with air resistance

It seems like I have been using my bullet model a lot lately. Each time I change it just a little. In this case, I am going to start with a .45 caliber bullet like the mythbusters did. They said they used it because it was heavy and slow. That is fine with me. Slow means that I can just use one value for the drag coefficient instead of my super-sonic coefficient table. If you want my python program, I will add it at the end. But here is my first run. I am going to shoot a .45 caliber bullet aimed horizontally 36 inches above the ground. Just as a comparison, I will plot the trajectory of the .45 and another object shot with it but without air resistance.