1. When two objects are moving in the same plane
and collide, linear momentum conservation can be
applied in a straightforward manner. If one of the
objects happens to be moving in the opposite
direction, we simply make one direction
_____________. Suppose the objects are not
moving parallel to one another?
CAN YOU SAY COMPONENTS!!!!
negative

2. m1v1x + m2v2x = m1V1x + m2V2x m1v1y + m2v2y = m1V1y + m2V2y
conservation of linear momentum in two dimensions
m1v1x + m2v2x = m1V1x + m2V2x
m1v1y + m2v2y = m1V1y + m2V2y

3. Vy= -9 m/s Vx= +10 m/s m 1v1x + m 2v2x = m 1 V1x + m 2V2x
Before
After
V1x = V2 x = ?
24 m/s
V1y = V2y = ? ?
m1 = 12 kg
m2 = 20 kg
16 m/s
v1x = 0 m/s
v1y = -24 m/s
v2x = +16 m/s
v2y = 0 m/s
m 1v1x + m 2v2x = m 1 V1x + m 2V2x
12(0)+ 20(16) = 12Vx + 20Vx
m 1v1y + m 2v2y = m 1V1y + m 2V2y
12(-24)+ 20(0) = 12Vy + 20Vy
Vy= -9 m/s
Vx= +10 m/s

4. θ = 42° 10 9 = 13.5 m/s @ 42°south of east R = (10)2 + (9)2
Use Pythagorean theorem to
determine the magnitude of
the resultant 9
R = (10)2 + (9)2
= 13.5 m/s
@ 42°south
of east
Use trigonometry to
determine the angle
(ALWAYS back at the beginning)
opp 9
tanθ = =
adj 10
θ = 42°

5. #2 is the same . . . . . just different
V1x = V2 x = ?
m1 = 15 kg
m2 = 19 kg
V1y = V2y = ?
v1x = +25 km/hr
v1y = 0 km/hr
v2x = 0 km/hr
v2y = -14 km/hr
m 1v1x + m 2v2x = m 1 V1x + m 2V2x
15(25)+ 19(0) = 15Vx + 19Vx
Vx= +11 km/hr
m 1v1y + m 2v2y = m 1V1y + m 2V2y
15(0)+ 19(-14) = 15Vy + 19Vy
Vy= -7.8 km/hr 11
= 13.5 km/hr
7.8
@ 35°south
of east

6. m 1v1x + m 2v2x + m 3v3x = m 1V1x + m 2V2x + m 3V3x
2.7 m/s
? m/s
v1x =
v1y =
v2x =
v2y =
v3x =
v3y =
V1x = +4 m/s
V1y = 0 m/s
V2x = 0 m/s
V2y = +2.7 m/s
V3x = ?
V3y = ?
4 m/s
Before
After
m1 = 2 kg
m2 = 3 kg
m3 = 4 kg
m 1v1x + m 2v2x + m 3v3x = m 1V1x + m 2V2x + m 3V3x
and
m 1v1y + m 2v2y + m 3v3y = m 1V1y + m 2V2y + m 3V3y

7. (back at the beginning)
0 = 2(4) + 3(0) + 4(V3x)
Add vectors 2
and
0 = 2(0) + 3(2.7) + 4(V3y) 2
V3x = -2 m/s and V3y = -2 m/s
Use trigonometry to
determine the angle
(back at the beginning)
Pythagorean theorem
R = (2)2 + (2)2
= 2.8 m/s
V = ° south of west
opp 2
tanθ = =
= 45°
adj 2

8. #4 – assume the eight ball is initially at rest.
assume the cue ball and eight ball have the same mass.
have phun! 4) ° south of east 5) ° east of north