Solution:To convert this measurement, we need to convert meters tomiles and seconds to hrs. To perform this, we require the followingrelationships:1000 meter = 1 kilometer; 1 kilometers = 0.621 mile; 60 seconds = 1 minute; 60 minutes = 1 hour; We can currently erected the equation making use of these relationships so the devices cancel out leaving only thewanted miles/hour.
You are watching: 2.998 x 10^8 m/s to km/hr
speedMPH = 2.998 x 10^8 m/sec x (1 km/1000 m) x (0.621 mi/1 km) x (60 sec/1 min) x (60 min/1 hr)
Keep in mind all the devices canceled out, leaving just miles/hr:>> speedMPH = (2.998 x 10^8 x 1/1000 x 0.621 x 60 x 60) miles/hr>> speedMPH = 6.702 x 10^8 miles/hr
Answer:The speed of light in miles per hour is 6.702 x 10^8 miles/hr.
edited Aug 30 at 5:04
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Rather than tackling the difficulty at hand also, here is a much easier instance. Suppose we start via a rate of 60 mph and want to convert to miles per minute. Due to the fact that 1 hour is 60 minutes, we have$$60 ext mph = frac60 ext miles1 ext hour = frac60 ext miles60 ext min = 1 ext mile/min.$$ Note that we have reput 1 hour by 60 minutes "by hand". This is reliable for a solitary unit conversion, yet appears tedious if multiple conversions had actually to be done. To make points even more helpful, we instead recreate the over computation as such:
$$60 ext mph = frac60 ext miles1 ext hour imesfrac1 ext hour60 ext minutes = 1 ext mile/min.$$
Note that we"ve exchanged "rearea 1 hour by 60 minutes" via "multiply by 1 hour / 60 minutes." The reason this works is because 1 hour = 60 minutes, so (1 hour)/(60 minutes) is just equal to one. So we multiplied 60 mph by 1, leaving the amount itself unchanged; but, the old systems cancel out in the process and also thereby bring out unit convariation.
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In this example, of course, the difficulty is straightforward enough that it doesn"t make a difference. But mean we wanted to transform 60 mph right into devices of feet per second. Because one mile is 5280 feet, one hour is 60 minutes, and one minute is 60 secs, we have the right to carry out all three unit conversions by the adhering to multiplication:
eginalign60 ext mph&= frac60 ext miles1 ext hour imes frac1 ext hour60 ext minutes imes frac1 ext minute60 ext seconds imes frac5280 ext feet1 ext mile\&= frac60 imes 528060 imes 60 frac extfeet extsecond\& = 88 ext ft/sec.endalign
Note how the multiplications are arranged to cancel out hours, minutes, and also miles.