To convert from yards per second to kilometers per hour, we need to follow several conversion steps. Let's break it down step by step:
1. Convert yards per second to feet per second: - There are 3 feet in 1 yard. - [tex]\( 1772 \text{ yards/second} \times 3 \text{ feet/yard} = 5316 \text{ feet/second} \)[/tex]
2. Convert feet per second to inches per second: - There are 12 inches in 1 foot. - [tex]\( 5316 \text{ feet/second} \times 12 \text{ inches/foot} = 63792 \text{ inches/second} \)[/tex]
3. Convert inches per second to centimeters per second: - There are 2.54 centimeters in 1 inch. - [tex]\( 63792 \text{ inches/second} \times 2.54 \text{ centimeters/inch} = 162031.68 \text{ centimeters/second} \)[/tex]
4. Convert centimeters per second to meters per second: - There are 100 centimeters in 1 meter. - [tex]\( 162031.68 \text{ centimeters/second} \div 100 \text{ centimeters/meter} = 1620.3168 \text{ meters/second} \)[/tex]
5. Convert meters per second to kilometers per second: - There are 1000 meters in 1 kilometer. - [tex]\( 1620.3168 \text{ meters/second} \div 1000 \text{ meters/kilometer} = 1.6203168 \text{ kilometers/second} \)[/tex]
6. Convert kilometers per second to kilometers per hour: - There are 3600 seconds in 1 hour. - [tex]\( 1.6203168 \text{ kilometers/second} \times 3600 \text{ seconds/hour} = 5833.14 \text{ kilometers/hour} \)[/tex]
7. Round the result to 3 decimal places: - The final result is already rounded to 2 decimals, so there's no need for extra rounding in this case.
So, [tex]\( 1772 \text{ yards/second} \)[/tex] is approximately [tex]\( 5833.140 \text{ kilometers/hour} \)[/tex].
