A Boat Has A Top Speed Of 32 Knots And A Displacement Of Approximately 98,000 Tons. Express The Top Speed In Miles Per Hour And The Displacement In Metric Tonnes (1 Knot = 1 Nautical Mile Per Hour, 1 Metric Tonne = 1000 Kilograms)
The Correct Answer and Explanation is :
To solve this problem, we need to convert both the top speed from knots to miles per hour and the displacement from tons to metric tonnes. Let’s break this down step-by-step:
Step 1: Converting Knots to Miles Per Hour (MPH)
1 knot is defined as 1 nautical mile per hour. A nautical mile is equal to 1.15078 miles. Therefore: 32 knots=32×1.15078 miles per hour32 \, \text{knots} = 32 \times 1.15078 \, \text{miles per hour} 32 knots=36.9265 miles per hour32 \, \text{knots} = 36.9265 \, \text{miles per hour}
Thus, the top speed of the boat is approximately 36.93 miles per hour.
Step 2: Converting Tons to Metric Tonnes
The displacement of the boat is given as 98,000 tons. The problem specifies that we need to convert this into metric tonnes. A “ton” here is likely a long ton, which is equal to 2,240 pounds. To convert from tons to metric tonnes (which is equivalent to 1,000 kilograms), we need to first convert the ton to pounds, then to kilograms, and finally to metric tonnes.
- First, convert tons to pounds:
98,000 , \text{tons} = 98,000 \times 2,240 , \text{pounds} = 219,520,000 , \text{pounds} ]
- Then convert pounds to kilograms (1 pound = 0.453592 kilograms):
219,520,000 , \text{pounds} = 219,520,000 \times 0.453592 , \text{kg} = 99,500,349.44 , \text{kg} ]
- Finally, convert kilograms to metric tonnes (1 metric tonne = 1,000 kilograms):
99,500,349.44 , \text{kg} = \frac{99,500,349.44}{1,000} , \text{metric tonnes} = 99,500.349 , \text{metric tonnes} ] Thus, the displacement of the boat is approximately 99,500.35 metric tonnes.
Final Answers:
- Top speed: 36.93 miles per hour
- Displacement: 99,500.35 metric tonnes
Explanation:
- Knots to Miles Per Hour: Since 1 knot equals 1 nautical mile per hour, and a nautical mile is about 1.15078 miles, the conversion factor is straightforward: multiply the speed in knots by 1.15078.
- Tons to Metric Tonnes: The conversion from tons to metric tonnes involves first converting tons to pounds (since long tons are typically in pounds), then converting pounds to kilograms, and finally dividing by 1,000 to convert kilograms to metric tonnes. This method ensures we account for the differences between the British long ton and the metric tonne.