CHAPTER 6. MOTIONIN TWO DIMENSIONS 6.3
For Player 2:
pix 2 = m 2 vi 2 x= 90× 8 × sin 60◦
piy 2 = m 2 vi 2 y= 90× 8 × cos 60◦
Step 3 : Now write down whatwe know about the final momentum:
For Player 1:
pfx 1 = m 1 vfx 1 = 90× vfx 1
pfy 1 = m 1 vfy 1 = 90× vfy 1
For Player 2:
pfx 2 = m 2 vfx 2 = 90× 0 = 0
pfy 2 = m 2 vfy 2 = 90× 0 = 0
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
0 + 90× 8 × sin 60◦ = 90× vfx 1 + 0
vfx 1 =
90 × 8 × sin 60◦
90
vfx 1 = 6. 928 ms−^1
piy 1 + piy 2 = pfy 1 + pfy 2
90 × 5 + 90× 8 × cos 60◦ = 90× vfy 1 + 0
vfy 1 =
90 × 5 + 90× 8 × cos 60◦
90
vfy 1 = 9. 0 ms−^1
Step 5 : Using the x and y components, calculatethe final total v
Use Pythagoras’s theorem to find the total final velocity:
θ
vfx 1
vfy
1
vftot
vftot =
�
v^2 fx 1 + v^2 fy 1
=
�
6. 9282 + 9^2
= 11. 36
