Collision problem, conservation of momentum

[Blue_Angel]

A particle of mass 3kg moving at 15ms^−1 collides with one of mass 2 kg moving at 5ms^−1 in the same direction. Calculate the velocities after the collision
i. the collision is elastic.
ii. Suppose that in the collision of part (i), the final velocities are not parallel to the initial velocities,

So I have the answer to part i: it's 7ms^-1 for 3kg particle and 17ms^-1 for the 2kg particle
I also have equations for the second part:
suppose for the 3kg particle its final velocity is v_1 at an angle to the horizontal of theta_1...

for momentum: 55=3*v_1*cos(theta_1)+2*v_2*cos(theta_2)
v_1*sin(theta_1)=v_2*sin(theta_2)
for kinetic energy: 725=3(v_1)^2+2(v_2)^2

Can anyone help me finish this by maximising the angle for v_1 i.e.theta_1

Thanks :)

 

[Simon Bridge]

Play with the relationships so you understand them ... how do the angles depend on each other? Is one of them always bigger than the other? Does one get bigger while the other gets smaller? Can either angle be 90deg?
This should help you figure out a strategy.

Basically you have 3 equations and 4 unknowns - so you will be expressing one of the unknowns in terms of another one ... there will be a range of values that satisfy the equation. You have to use your understanding to pick an appropriate relationship to maximize.