When are final velocities perpendicular in a collision where one mass is at rest?

[ShayanJ]

Imagine a point mass m1 collides a mass m2 and m2 is at rest.In what condition the final velocity of two masses,will be prependicular to each other?
thanks

 

[tiny-tim]

Hi Shyan!

(try using the X₂ icon just above the Reply box )

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[ShayanJ]

I just have the formulas relating the magnitude of final and initial velocities in one dimension but,as you can see,this problem is two dimensional.

 

[tiny-tim]

yes, the energy formula is one-dimensional,

but the momentum formula is a vector formula, so it's as many dimensions as there are …

in this case, you can write the momentum formula twice, for the x and y directions separately …

what do you get? ​

 

[ShayanJ]

And then make two systems of equations one with energy equation and x momentum equation and one with energy equation and y momentum equation?

 

[tiny-tim]

it's not really two systems, it's just three equations …

try it and see! ​