You have three equations
momentum to the right/left
momentum up/down
conservation of energy
Two unknowns: Va and Vb.
on the momemtum up/down, write it as a function of Va and Vb times sinAngle
one the momentum right/left, use Va and Vb times Cosangle.
It will solve, the algebra is messy at times
A stationary billiard ball, mass 0.17 kg, is struck by an identical ball moving at 2.7 m/s. After the collision, the second ball moves off at 60° to the left of its original direction. The stationary ball moves off at 30° to the right of the moving ball's original direction. What is the speed of each ball after the collision?
3 answers
I'm sorry, but that doesn't make sense to me, is there any other way you can explain it?
Thanks.
Thanks.
They are asking for only two unknowns although three equations could be applied. You can solve the problem just by using momentum conservation, but presumably kinetic energy will also be conserved, if the angles they provided are correct. (Billiard ball collisions are very elastic)
M Vo = M Va cos 30 + M Vb cos 60
0 = M Va sin 30 - M Vb sin 30
Vo = 0.866 Va + 0.500 Vb
0.500 Va = 0.866 Vb
Vo = 0.866 Va+(0.250/0.866)Va
= 1.1546 Va
Va = 0.866 Vo
Vb = 0.500/0.866 * 0.866 Vo = Vo/2
Note that Va^2 + Vb^2 = Vo^2, so energy is indeed conserved.
M Vo = M Va cos 30 + M Vb cos 60
0 = M Va sin 30 - M Vb sin 30
Vo = 0.866 Va + 0.500 Vb
0.500 Va = 0.866 Vb
Vo = 0.866 Va+(0.250/0.866)Va
= 1.1546 Va
Va = 0.866 Vo
Vb = 0.500/0.866 * 0.866 Vo = Vo/2
Note that Va^2 + Vb^2 = Vo^2, so energy is indeed conserved.
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