- #1

Arejang

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## Homework Statement

Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide with a glancing blow. Asteroid A, which was initially traveling at 40.0 m/s, is deflected 30.0[tex]\circ[/tex] from its original direction, while asteroid B travels at 45.0 [tex]\circ[/tex] to the original direction of A

Find the speed of asteroid A and asteroid B after the collision.

What fraction of the original kinetic energy of asteroid A dissipates during this collision?

## Homework Equations

Conservation of Kinetic energy

[tex]1/2m_{a}v_{a1x}^{2}+1/2m_{b}v_{b1x}^{2}=1/2m_{a}v_{a2x}^{2}+1/2m_{b}v_{b2x}^{2}[/tex]

Conservation of momentum

[tex]m_{a}v_{a1x}+m_{b}v_{b1x}=m_{a}v_{a2x}+m_{b}v_{b2x}[/tex]

## The Attempt at a Solution

I really want to assume that asteroid B is initially at rest, but since it's not stated; I'm not sure I should do so. But for this problem, I feel like it may be the only way to solve this problem so that's what I will assume, please correct me if I'm wrong. Anyway, it seems like you would have to solve for one of the final velocities through substitution. Since the masses of the two asteroids are the same, we can factor them out of both equations, leaving us with only the velocities to worry about.

So our Kinetic Energy Conservation formula looks like this:

[tex]1/2v_{a1x}^{2}+1/2v_{b1x}^{2}=1/2v_{a2x}^{2}+1/2_{b2x}^{2}[/tex]

I then proceeded to solve for [tex]v_{a2x}[/tex] and got

[tex]v_{a2x}=\sqrt{v_{b2x}^{2}-v_{a1x}^{2}}[/tex]

This expression of [tex]v_{a2x}[/tex] I subbed into the momentum conservation formula, getting:

[tex]v_{a1x}=v_{b2x}+\sqrt{v_{b2x}^{2}-v_{a1x}^{2}[/tex]

It seems logical that I solve for the velocity of asteroid B, then plug that in the kinetics formula then solve for A, but I'm not certain how to integrate the angle of the collisions into each formula. In fact, I'm actually not sure if I even approached this problem correctly. But please let me know where I need to go with this.

Oh and to Doc. Al if you're reading this, it turned out my previous problem was correct and that the online problem had the wrong answer input as the correct one. Consequently, everyone got full credit for the problem.