Final answer:
The total momentum of all pieces after the firework explodes is calculated using the conservation of momentum law, yielding a total momentum of 37.5 kg·m/s, based on the initial mass and velocity of the firework.
Step-by-step explanation:
The total momentum of all pieces after the firework explodes can be found using the law of conservation of momentum. This law states that the total momentum of a closed system does not change in the absence of external forces. Since the firework is shot straight up and there are no horizontal forces acting on it, its momentum just before the explosion is the same as the total momentum of all the pieces after the explosion.
The momentum p of the firework before the explosion can be calculated using the formula p = m × v, where m is the mass and v is the velocity. In this case, the mass m is 1.5 kg and the velocity v is 25 m/s. So, p = 1.5 kg × 25 m/s = 37.5 kg·m/s. This is the total momentum of all the pieces after the firework explodes as well.