264 Linear Momentum and CollisionsP9.33By conservation of momentum for the system of the two billiardballs (with all masses equal),500043330012504 3330 021625060022222..cos...sin..msms at+=°+==°+=−°bgvvvvfxfxfyfyfvFIG. P9.33Note that we did not need to use the fact that the collision is perfectly elastic.P9.34(a)ppif=soxixf=andyiyf=mvmvmvi=+coscosθφ(1)0mvmvsinsin(2)From (2), sinsinso Furthermore, energy conservation for the systemof two protons requires121212222mvmvmvisovvi=2FIG. P9.34(b)Hence, (1) givesvvii=22cosθ45 0.φ°45 0.P9.35mmmmiif112212vvv+:3 00 5 006 005 00±.±.afijv−=vij120.±.±ejP9.36x-component of momentum for the system of the two objects:
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