Trigonometry Problem: Solving for Unknowns in a Collision Scenario

[henryc09]

Homework Statement

In a certain collision problem the kinematics are determined by the following three equations:

u=u1cos(@) + SQRT(2) * u2
u1sin(@)=SQRT(2) * u2
0.5mu^2=0.5mu1^2 + 0.5(2m)u2^2

Use the first two equations to express u1 and u2 in terms of u, sin(@) and cos(@). Then substitute in the third equation and obtain solutions for sin(@).

Homework Equations

see above

The Attempt at a Solution

I have that u1=u/(sin(@)+cos(@) and u2=u/(SQRT(2)((cos(@)/sin(@))+1) and substitute those into the third equation eliminating U and m, but having tried various methods cannot solve the trigonmetry equation. Any help would be greatly appreciated.

 

[kuruman]

u=u1cos(@) + SQRT(2) * u2
u2sin(@)=SQRT(2) * u2
0.5mu^2=0.5mu1^2 + 0.5(2m)u2^2

This equation is confusing. I can divide both side by u2 and get sin(@)=SQRT(2) which can't be true.

 

[henryc09]

This equation is confusing. I can divide both side by u2 and get sin(@)=SQRT(2) which can't be true.

Oops sorry, it should be u1sin(@)=SQRT(2)u2

 

[kuruman]

OK. Now tell me what the unknown quantities are and what the known quantities are. In other words, we are solving for what in terms of what?