## College Physics (4th Edition)

The speed of the third piece is $170~m/s$
Just before the firecracker explodes, the speed is zero, and so the initial momentum is zero. By conservation of momentum, the final momentum is also zero. Let $M$ be the mass of each of the three pieces. We can find the magnitude of the vector sum of the momentum of the two pieces moving with a speed of $120~m/s$ at right angles to each other. $\sqrt{[(120~m/s)~M]^2+[(120~m/s)~M]^2} = (170~m/s)~M$ For the vector sum of the momentum of all three pieces to equal zero, the third piece must of a momentum of $(170~m/s)~M$ in the opposite direction. We can find the speed of the third piece: $Mv = (170~m/s)~M$ $v = 170~m/s$ The speed of the third piece is $170~m/s$.