Conservation of momentum in an oblique launch and projectile explosion

  • #1
TheGreatDeadOne
22
0
Homework Statement
A projectile of mass m is fired with initial velocity of module v_0 at an elevation angle of 45◦. The projectile explodes in the air in two pieces of masses m/3 and 2m/3. The pieces continue to move in the same plane as the entire projectile and reach the ground together. The smaller piece falls at a distance of 3(v_0)^2 /2g from the launch point. Determine the range of the largest chunk. Neglect air resistance
Relevant Equations
..
This problem I already solved using another resource (just get the coordinate of the center of mass reach and from it, get to the larger mass. R = (3v02) / (4g)). But I'm having some trouble calculating using moment conservation. Here what I've done so far:



As the fragments fall in the same time interval, the vertical components of their velocities are the same, since in the act of the explosion, they depart from the same height:


In addition, we can equalize the fall time intervals of each fragment using the horizontal component of each fragment (uniform movement):


Range:


 
Last edited:
Physics news on Phys.org
  • #2
I don't understand what you're doing. You could use the centre of horizontal momentum frame. Also, the y-momentum can be taken out of the equations, because of the equal time condition, leaving you to focus on the x-momentum.
 
  • #3
PeroK said:
I don't understand what you're doing. You could use the centre of horizontal momentum frame. Also, the y-momentum can be taken out of the equations, because of the equal time condition, leaving you to focus on the x-momentum.
I used the center of horizontal momentum frame. I just used the y-moment to find the angle of the velocity component, so I can write the velocity in the horizontal direction. I'll edit the equations to make it clearer
 
  • #4
TheGreatDeadOne said:
I used the center of horizontal momentum frame. I just used the y-moment to find the angle of the velocity component, so I can write the velocity in the horizontal direction. I'll edit the equations to make it clearer
I think if you are given , then in a problem like this you should be using .
 
  • #5
TheGreatDeadOne said:


In addition, we can equalize the fall time intervals of each fragment using the horizontal component of each fragment (uniform movement):

If I have correctly understood what you are doing, I think your key mistake is sayingThis implies the x-component of ’s momentum is unchanged by the explosion – as if the original mass divided into two but the two parts didn’t move apart. But, for example, a significant release of energy in the explosion could make any value, whereas would be unaffected.

For informationshould be(But this is just a typo'.)
 
  • Like
Likes TheGreatDeadOne
Back
Top