Two billiard balls undergo a glancing collision. Before the collision the first ball was travelling east at 2.6 m/s and the second ball was travelling west at 1.2 m/s. If the second ball is deflected by +90 degrees travelling north at 1.47 m/s, what is the speed of the first ball after the collision?
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assuming that the two balls have the same mass, m
then
momentum before = 1.4m, E
so the momentum after the collision will be the same
draw a parallelogram with 1.47m, N as a side
and 1.4m, E as the diagonal
solve for the other side
or
1.4m@90 - 1.47m@0 = 2.03m@136.4
or 2.03 m/s, 36.4 deg S of E
now the curious part
billiard ball collisions are essentially elastic
so
energy will also be conserved (or practically so)
but
the results show a considerable change in energy
so this collision is ostensibly very far from being elastic
then
momentum before = 1.4m, E
so the momentum after the collision will be the same
draw a parallelogram with 1.47m, N as a side
and 1.4m, E as the diagonal
solve for the other side
or
1.4m@90 - 1.47m@0 = 2.03m@136.4
or 2.03 m/s, 36.4 deg S of E
now the curious part
billiard ball collisions are essentially elastic
so
energy will also be conserved (or practically so)
but
the results show a considerable change in energy
so this collision is ostensibly very far from being elastic