To compare the momentum of the two vessels, we can use the formula for momentum, which is:
\[ \text{Momentum} = \text{mass} \times \text{velocity} \]
For the fishing boat:
- Mass = 100 tons = 100,000 kg (since 1 ton = 1,000 kg)
- Velocity = 30 knots = 30 × 0.51444 m/s = 15.432 m/s (approximately)
Calculating the momentum of the fishing boat: \[ \text{Momentum}_{\text{boat}} = 100,000 , \text{kg} \times 15.432 , \text{m/s} \approx 1,543,200 , \text{kg m/s} \]
For the larger ship:
- Mass = 3000 tons = 3,000,000 kg
- Velocity = 10 knots = 10 × 0.51444 m/s = 5.1444 m/s (approximately)
Calculating the momentum of the larger ship: \[ \text{Momentum}_{\text{ship}} = 3,000,000 , \text{kg} \times 5.1444 , \text{m/s} \approx 15,433,200 , \text{kg m/s} \]
Comparison:
- Momentum of the fishing boat: \( \approx 1,543,200 , \text{kg m/s} \)
- Momentum of the larger ship: \( \approx 15,433,200 , \text{kg m/s} \)
Thus, the 3000-ton ship going 10 knots has significantly more momentum than the 100-ton fishing boat going 30 knots.