Elastic collision between two billiard balls

AI Thread Summary
In the discussion about an elastic collision between two billiard balls, the problem involves two balls with masses of 0.4 kg and 0.3 kg, where the first ball has an initial velocity of 3 m/s and the second is at rest. After the collision, the first ball's velocity is reduced to 1.5 m/s, while the second ball's final velocity and angles need to be determined. The conservation of kinetic energy and momentum principles are applied to find the unknowns. The main challenge arises in solving for the angles due to the presence of sine and cosine terms in the momentum equations. A suggestion is made to use a trigonometric identity to relate the sine and cosine functions for a solution.
phyme814
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Homework Statement


Two balls collide on a frictionless surface. Mass m1 = .4 kg and Mass m2 = .3 kg . The initial velocity of m1 is 3 m/s. While m2 is at rest. After the collision the velocity of m1 is 1.5 m/s, θ1 above the horizontal. While m2 gains an unknown velocity of v2f, θ2 below the horizontal.
Find v2f, θ1, and θ2


Homework Equations



Conservation of kinetic energy
Conservation of momentum

The Attempt at a Solution


I can find v2f, but I am having trouble with finding the angles.
 
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phyme814 said:
I can find v2f, but I am having trouble with finding the angles.
Show what you did.
 
I presume you used conservation of energy to solve for v2f. Now use conservation of momentum to solve for the angles. (You'll get two equations and two unknowns.)
 
Yepp I used conservation of kinetic energy.
I was using the conservation of momentum equation for the unknowns of the angles but I was running into trouble because I would get sinθ1 and sinθ2 in one equation and cosθ1 and cosθ2 in the other equation.
 
phyme814 said:
but I was running into trouble because I would get sinθ1 and sinθ2 in one equation and cosθ1 and cosθ2 in the other equation.
Sine and cosine can be related by a trig identity.
 

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