CHAPTER 6. MOTIONIN TWO DIMENSIONS 6.3
Step 2 : Use conservation of momentum to solve the problem. First find
the initial total momentum:
Total initial momentum= Total final momentum.
But we have a two dimensional problem, and weneed to break up
the initial momentum into x and y components. Remember that
momentum is a vectorand has direction whichwe will indicate
with a ’+’ or ’-’ sign.
pix = pfx
piy = pfy
For Player 1:
pix 1 = m 1 vi 1 x= 80× (−5)× cos 75◦
piy 1 = m 1 vi 1 y= 80× 5 × sin 75◦
For Player 2:
pix 2 = m 2 vi 2 x= 80× 6 × cos 60◦
piy 2 = m 2 vi 2 y= 80× 6 × sin 60◦
Step 3 : Now write down whatwe know about the final momentum:
For Player 1:
pfx 1 = m 1 vfx 1 = 80× vfx 1
pfy 1 = m 1 vfy 1 = 80× vfy 1
For Player 2:
pfx 2 = m 2 vfx 2 = 80× (− 0 .3)
pfy 2 = m 2 vfy 2 = 80× 6
Step 4 : Use conservation of momentum:
The initial total momentum in the x direction is equal to thefinal
total momentum in the x direction.
The initial total momentum in the y direction is equal to thefinal
total momentum in the y direction.
If we find the final x and y components, then we can find the final
total momentum.
pix 1 + pix 2 = pfx 1 + pfx 2
− 80 × 5 cos 75◦+ 80× 6 × cos 60◦ = 80× vfx 1 + 80× (− 0 .3)
vfx 1 =
− 80 × 5 cos 75◦+ 80× 6 × cos 60◦
80
−
80 × (− 0 .3)
80
vfx 1 = 2. 0 ms−^1
piy 1 + piy 2 = pfy 1 + pfy 2
80 × 5 × sin 75◦+ 80× 6 × sin 60◦ = 80× vfy 1 + 80× 6
vfy 1 =
80 × 5 sin 75◦+ 80× 6 × sin 60◦
80
−
80 × 6
80
vfy 1 = 4. 0 ms−^1
