Final answer:
The velocity of the board relative to the ice is 0.829 m/s in the opposite direction of the boy's movement, which is calculated using the principle of conservation of momentum.
Step-by-step explanation:
To find the velocity of the wood board relative to the ice, we must use the principle of conservation of momentum. Since the system is isolated and there are no external forces acting on it, the total momentum before and after the boy starts walking must remain the same. Initially, the total momentum is zero because both the boy and the board are at rest relative to the ice.
Once the boy walks with a velocity of 1.47 m/s relative to the ice, the board must move in the opposite direction to conserve momentum. Let's denote the velocity of the board as V. The momentum of the boy is the product of his mass and velocity, so we have:
- Momentum of the boy: 35.7 kg × 1.47 m/s = 52.48 kg·m/s (in the positive direction)
- Momentum of the board: 63.3 kg × V (in the negative direction)
To find the board's velocity, we set up the equation:
35.7 kg × 1.47 m/s = 63.3 kg × V
Rearranging to solve for V, we find:
V = (35.7 kg × 1.47 m/s) / 63.3 kg
V = 52.48 kg·m/s / 63.3 kg
V = 0.829 m/s (in the negative direction)
Thus, the velocity of the board relative to the ice is 0.829 m/s in the direction opposite to the boy's movement.