- #1

amanda.ka

- 46

- 0

## 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 + m2v2

_{i}= m1v1 + m2v2

_{f}

(0.5)(4) = (0.5)(2cosθ) + (0.3)(4.47cosφ)

**2 = cosθ + 1.341cosφ**

Y DIRECTION: Pi = Pf

m1v1 + m2v2

_{i}= m1v1 + m2v2

_{f}

0 = (O.5)(2sinθ) -(0.3)(4.47sinφ)

**0 = sinθ - 1.341sinφ**