Final answer:
To find the speed and direction of the other piece, we can use the law of conservation of momentum. The other piece has a velocity of -51.43 m/s to the left.
Step-by-step explanation:
To find the speed and direction of the other piece, we can use the law of conservation of momentum. Since the initial momentum of the firecracker is zero (as it was launched vertically), the total momentum after the explosion must also be zero. The momentum of the 72-g piece can be calculated as mass times velocity, which is (72 g)(20 m/s) = 1440 g*m/s. To have a total momentum of zero, the other piece must have a momentum of -1440 g*m/s, which means it has a velocity of -1440 g*m/s divided by its mass. The total mass of the firecracker is 100 g, so the other piece has a mass of (100 g - 72 g) = 28 g. Therefore, the velocity of the other piece is (-1440 g*m/s) / (28 g) = -51.43 m/s. Since it is projected horizontally to the left, the speed and direction of the other piece is 51.43 m/s to the left, which is approximately 51 m/s to the left.