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## Homework Statement

Particle A has mass m and initial velocity v0. A collides with particle B, which has mass M and is initially at rest. After the collision, the particles follow the paths shown in the figure. Calculate φ in degrees, for an ideal elastic collision.

Data: m = 0.7 kg; M = 4.7 kg.

http://imgur.com/UcZciBB

θ=45

## Homework Equations

K=[itex]\frac{1}{2}[/itex]m

_{1}v

_{1}

^{2}

## The Attempt at a Solution

I'm not sure of the most effective route here. I have three equations but I have four unknowns (v

_{1}, v

_{1}', v

_{2}', and [itex]\phi[/itex])

First I have momentum in the x direction:

m

_{1}v

_{1}=[itex]\frac{1}{2}[/itex]m

_{1}v

_{1}'cos[itex]\phi[/itex]+m

_{2}v

_{2}'cosθ

Second I have momentum in the y direction:

0=m

_{1}v

_{1}'sin[itex]\phi[/itex]-m

_{2}v

_{2}'sin[itex]\theta[/itex]

or

m

_{1}v

_{1}'sin[itex]\phi[/itex]=m

_{2}v

_{2}'sin[itex]\theta[/itex]

Lastly I have the conservation of kinetic energy since this is an elastic collision.

[itex]\frac{1}{2}[/itex]m

_{1}v

_{1}

^{2}=[itex]\frac{1}{2}[/itex]m

_{1}v

_{1}'

^{2}+[itex]\frac{1}{2}[/itex]m

_{2}v

_{2}'

^{2}

I'm not sure of another equation that would help me find reduce this and solve for [itex]\phi[/itex]. Does anyone have any suggestions?

Thank you!