1. Section 9.4: Collisions in 2 Dimensions

2. Elastic Collisions in 2Dimensions
 v2i = 0
before
Physical Principles:
Same as in 1Dimension
1. VECTOR momentum conservation
m1v1ix + m2v2ix = m1v1fx + m2v2fx
m1v1iy + m2v2iy = m1v1fy + m2v2fy or
m1v1i + 0 = m1v1f cosθ + m2v2fx cosφ
0 = m1v1fsinθ - m2v2fsinφ
2. Kinetic Energy Conservation
(½)m1(v1i)2 + (½)m2(v2i)2 = (½)m1(v1f)2 + (½)m2(v2f)2
after

3. Ex. 9.4: 2 Car Collision at Intersection
m1 = 1,500 kg, v1i = 25 m/s to the East
 v1i = v1ix = 25 m/s, v1iy = 0
m2 = 2,500 kg, v2i = 20 m/s to the North
 v2ix = 0, v2i = v2iy = 20 m/s
Collision is perfectly inelastic
So, cars stick together! θ = φ, v1f = v2f
Find final velocities
Momentum conservation:
x: m1v1ix + m2v2ix = m1v1fx + m2v2fx
or m1v1i + 0 = (m1 + m2)vf cosθ (1)
y: m1v1iy + m2v2iy = m1v1fy + m2v2fy
0 + m2v2i = (m1+ m2)vfsinθ (2)
(1) & (2) are 2 equations, 2 unknowns! Use algebra to solve!
Results: vf = 15.6 m/s, θ = 53.1º (North of East)