- #1
amanda.ka
- 46
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Homework Statement
A 2D elastic collision:
Two pucks (masses m1 = 0.5 kg and m2 = 0.3 kg) collide on a frictionless air-hockey table. Puck 1 has an initial velocity of 4 m/s in the positive x direction and a final velocity of 2 m/s in an unknown direction, θ. Puck 2 is initially at rest. Find the final speed of puck 2 and the angles θ and φ.
I get stuck at the end of this problem when I have to use the two equations to solve for 2 unknown angles. If someone could show me how to do that last step that would be great. Thanks in advance!
Homework Equations
The Attempt at a Solution
Since the collision is elastic I found the final kinetic energy using Ei = Ef and it equals 4.47 m/s
Then conservation of the x and y components of total momentum:
X DIRECTION: Pi = Pf
m1v1 + m2v2i = m1v1 + m2v2f
(0.5)(4) = (0.5)(2cosθ) + (0.3)(4.47cosφ)
2 = cosθ + 1.341cosφ
Y DIRECTION: Pi = Pf
m1v1 + m2v2i = m1v1 + m2v2f
0 = (O.5)(2sinθ) -(0.3)(4.47sinφ)
0 = sinθ - 1.341sinφ