If a stationary object explodes into two pieces, how can momentum be conserved if both pieces are moving?
Because they move in opposite directions. If a 2 kg object explodes into two 1 kg pieces, one moving left at 10 m/s and one right at 10 m/s, their momenta are –10 kg·m/s and +10 kg·m/s—which sum to zero, matching the initial momentum. The calculator visualises this perfectly.
