Help with Physical Vector problem

[Timothy S]

This is a repost because i realized i put it on the wrong forum section.

After getting Kleppner and Kolenkow's second edition textbook I began my exploration of physics. I'm a sophomore in high school and VERY ignorant in regards to physics so if this question make no sense set me straight. I would appreciate it you told me what mistakes I made throughout the problem and how you would solve it.

I devised the following problem for myself:

Asteroid 1 with a Mass of 300 Kg and a Velocity of V = (20i + 4j - 12z) collides with Asteroid 2 with a Mass of 1800 Kg and a Velocity of V = (-3i - 16j -32z). What is the Angle between the two Asteroids after the collision? What are the two Asteroid's velocities after the collision?

1. I found the Momenta of the two asteroids. (P1 is Asteroid one's momentum. P2 is Asteroid two's momentum.)

Because mass is a scalar quantity, I multiplied the Components of velocity by Mass.

P1 = 300(20i + 4j - 12z) = (6000i + 1200j - 12k)

P2 = 1800(-3i - 16j - 32z) = (-5400i - 28800j - 57600k)

2. Then I got the Angle between the two Momenta Vectors.

cos (θ) = (P1 ⋅ P2) / |P1||P2| = 72.18°
My problem is that i don't know how to obtain the Asteroid's momentum or Velocity after the collision.

 

[Joshua L]

You requested that you should be set straight, so excuse me for my corrections.

P1 = 300(20i + 4j - 12z) = (6000i + 1200j - 12k)

You did not multiply the mass to the z-component of Asteroid's velocity; it should be

P1 = (6000i + 1200j - 3600k) kg m/sec

Asteroid 1 with a Mass of 300 Kg and a Velocity of V = (20i + 4j - 12z) collides with Asteroid 2 with a Mass of 1800 Kg and a Velocity of V = (-3i - 16j -32z). What is the Angle between the two Asteroids after the collision? What are the two Asteroid's velocities after the collision?

My problem is that i don't know how to obtain the Asteroid's momentum or Velocity after the collision.

There are too many unknowns that are needed to answer your specific question. For example, was the collision inelastic? Was it elastic? Did the asteroids break apart into significantly massive pieces? Do you know the momentum of one asteroid after the collision? From what you were given so far, the problem can't be solved until you have more information.

 

[Timothy S]

Thank you. I multiplied the z component on paper i just forgot to type it up. the collision is inelastic. I didn't know you you needed one of the Asteroid's momentum after the impact, it seems like there is plenty of information to derive each Asteroid's velocity without it.

 

[NascentOxygen]

To turn this into a legitimate exercise, imagine that the smaller body cleanly embeds itself into the larger one---determine the velocity of the combination. What change in speed has the larger body undergone?

 

[Joshua L]

Now it can be done; this is an example of a perfectly inelastic collision. The sum of the initial momentum of the two asteroids would equal the momentum of the combined asteroid after the collision. Now you would have enough information to solve the problem.

 

[Timothy S]

thank you. I think I know what you mean.