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cereal9

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## Homework Statement

Two objects with masses m1 and m2 are traveling in a frictionless surface and will collide perpendicular to each other (m1 is moving on the +x-axis, m2 is moving on the +y-axis). The distances of objects m1 and m2 from the collision point are d1 and d2 respectively.

Q: What Δv is required for m2 to avoid collision with m1 by a distance x?

http://dl.dropbox.com/u/12084119/image.PNG

## Homework Equations

[tex]t=\frac{d}{v}[/tex]

[tex]x=v_0t+\frac{1}{2}at^2[/tex]

## The Attempt at a Solution

So I'm having a bit of trouble understanding how to attack this problem. I think I'm lacking some fundamental understanding of kinematics.

- For m2 to collide with m1,

[tex]t_1=t_2[/tex]

[tex]\frac{d_1}{v_1}=\frac{d_2}{v_2}[/tex]

- For m2 to miss collision with m1 by a distance x I think that this has to be true,

[tex]t_2new=t_1new[/tex]

[tex]t_2new=\frac{d_1+x}{v_1}[/tex]

In my previous attempt I'd tried to solve for a new velocity required for m2 to travel the distance d2 like so:

[tex]v_2new=\frac{d_2v_1}{d_1+x}[/tex]

[tex]Δv_2=v_2new-v_2[/tex]

But this is not correct, since this would imply that there would be an immediate change in velocity when there should be an an acceleration to achieve that velocity.

So I know I need a time value for m2 and also an acceleration, which brings me to this:

[tex]d_2=v_2t_2+\frac{1}{2}a_2t^2_2[/tex]

I'm stuck on how to figure out both a2 and t2 to allow for this collision to not occur. Or rather, for a new "collision" to occur where object m1 has already passed a distance of x by the time mass m2 arrives at the previous impact location. Any and all help is appreciated, I'm really stumped!

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