Question

When Coast Guard pararescue jumpers leap from a helicopter to save a person in the water, they like to jump when the helicopter is flying "ten and ten," which means it is 10 feet above the water and moving forward with a speed of 10 knots. What is "ten and ten" in SI units? (A knot is 1 nautical mile per hour, and a nautical mile is \(1.852 \mathrm{~km}\).)

Short answer

"Ten and ten" means 3.048 meters and 5.144 meters/second.

Step-by-step solution

Convert Height from Feet to Meters

The helicopter is 10 feet above the water. We need to convert feet to meters. The conversion factor is 1 foot = 0.3048 meters.To convert, calculate:\[ 10 ext{ feet} \times 0.3048 \text{ meters/foot} = 3.048 ext{ meters} \]

Convert Speed from Knots to Meters per Second

The helicopter is moving at 10 knots. A knot is defined as 1 nautical mile per hour, and a nautical mile is equal to 1.852 km.First, convert 10 knots to kilometers per hour:\[ 10 ext{ knots} \times 1.852 ext{ km/knot} = 18.52 ext{ km/h} \]Next, convert kilometers per hour to meters per second. There are 1000 meters in a kilometer and 3600 seconds in an hour:\[ 18.52 ext{ km/h} \times \frac{1000 ext{ meters}}{3600 ext{ seconds}} = 5.144 ext{ meters/second} \]

Key concepts

Height Conversion

Converting height measurements from feet to meters is a common task, especially when dealing with scientific data or international communication, as the metric system is widely used globally. Consider that when you are given a height in feet, to convert it to meters, you simply use the conversion factor: 1 foot equals 0.3048 meters.

• Start with the height in feet, which is 10 feet in this scenario.
• Multiply the number of feet by the conversion factor: 10 feet × 0.3048 meters/foot.
• This results in 3.048 meters.

This straightforward multiplication gives the height in meters, making it compatible with SI units, which is crucial for scientific consistency and precision.

Speed Conversion

Speed conversion is essential when translating speeds from units like knots, often used in maritime and aviation contexts, to common metric units such as meters per second (m/s). Today, we manage this conversion simply by using a series of straightforward steps.

First, acknowledge that a knot is equivalent to 1 nautical mile per hour. Remember, a nautical mile equals 1.852 kilometers. Therefore:

• Convert knots to kilometers per hour: 10 knots × 1.852 km/knot = 18.52 km/h.
• Next, convert kilometers per hour to meters per second. Do this using the conversions of 1000 meters/kilometer and 3600 seconds/hour.
• Perform the calculation: 18.52 km/h × (1000 meters/3600 seconds) = 5.144 meters/second.

Understanding these conversions helps ensure that data is communicated effectively across different systems.

Metric System

The metric system, an international decimalized system of measurement, provides a standard for measuring distance, volume, mass, and more. It's used by most countries around the world, promoting uniformity and facilitating international trade and scientific cooperation.

This system is based on units such as meters for length, kilograms for mass, and seconds for time, which together form the SI (International System of Units). Its advantages include simplicity due to its base-10 structure, which makes conversions straightforward compared to other measurement systems.

• It eliminates the need for intricate conversions such as those found in the imperial system (inches to feet, yards to miles).
• This helps in scientific environments where clear communication and precision are paramount.

The transition to this universal system leads to improved consistency, enhancing understanding and reducing errors in communication and data exchange.