Finding Distance of Fragment After Shell Explosion - Center of Mass

[Twigs]

Although this seems simple, I don't think I'm reading the problem right. Currently we are studying center of mass such as the velocity and position of the center of mass. The problem is a shell is fired from a gun with a muzzle velocity of 1500ft/s at an angle of 60 degrees with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed is immediately after the explosion is zero, falls vertically. How far from the gun does the other fragment land, assuming level terrain.

Im having trouble understanding how center of mass can be used in the problem. Any help getting me started with the problem is greatly appreciated.

 

[vsage]

The center of mass travels along the path that the shell would have taken had it held together (in a perfect world). Given the path that one fragment takes, you can find the trajectory of the other fragment. These two fragments must sum to the trajectory of the original shell (center of mass of the system). I hope this helps.

 

[wais]

Hello,

I can understand your confusion with this problem. It may seem simple at first, but it involves applying the concept of center of mass in a real-world scenario. Let's break down the problem step by step to help you better understand it.

Firstly, the concept of center of mass tells us that the average position of all the mass in a system is considered as the center of mass. In this problem, we have a shell that explodes into two fragments, each with equal mass. This means that the center of mass of the system remains at the same position even after the explosion.

Now, the problem mentions that one of the fragments falls vertically with zero initial velocity. This means that the other fragment will have some initial velocity after the explosion, but its center of mass will still remain at the same position as before the explosion.

We can use the equation for center of mass, which is given by:

Center of mass = (m1 * r1 + m2 * r2) / (m1 + m2)

where m1 and m2 are the masses of the two fragments and r1 and r2 are their respective positions from the origin (in this case, the gun).

Since the center of mass remains at the same position, we can equate the center of mass before and after the explosion. This gives us the equation:

(m1 * r1 + m2 * r2) / (m1 + m2) = (m1 * 0 + m2 * d) / (m1 + m2)

where d is the distance traveled by the other fragment after the explosion. Solving this equation will give us the value of d, which is the distance from the gun where the other fragment lands.

I hope this explanation helps you understand how center of mass can be used in this problem. Remember, the key concept here is that the center of mass remains at the same position even after the explosion. Good luck!