Final answer:
After the arrow is fired, the person moves across the ice with a velocity of -0.417 m/s.
Step-by-step explanation:
When the person shoots the arrow horizontally, there is no vertical change in momentum. According to the law of conservation of momentum, the total initial momentum of the person and the bow-arrow system is equal to the total final momentum. Since the arrow has a mass of 0.50 kg and initial velocity of 50.0 m/s, its initial momentum is 0.50 kg * 50.0 m/s = 25.0 kg·m/s.
The person and bow have a mass of 60.0 kg and an initial velocity of zero. To find the final velocity of the person, we can use the equation m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2', where m1 and m2 are the masses, v1 and v2 are the initial velocities, and v1' and v2' are the final velocities. Since the person initially has zero velocity, the equation simplifies to m2 * v2 = m2 * v2'. Rearranging the equation, we get v2' = v2 = 25.0 kg·m/s / 60.0 kg = 0.417 m/s. Therefore, the person moves across the ice with a velocity of -0.417 m/s.