Question #f5cc7
2 Answers
Its speed is 1206 mph.
Explanation:
This is an exercise in unit conversions.
In this question, we must somehow convert metres to miles and seconds to hours.
The conversions I remember are
#"1 m = 39.37 in"# #"12 in = 1 ft"# #"5280 ft = 1 mi"# #"60 s = 1 min"# #"60 min = 1 h"#
Let's put these all together.
Explanation:
I will use four conversion factors here, two to convert the distance from meters to miles and two to convert the time from seconds to hours.
More specifically, I will use
#"1 km" = 10^3"m" " "# and#" " "1 mi " = " 1.609344 km"#
#"1 min " = " 60 s" " "# and#" " "1 hr " = " 60 min"#
I'll add the conversion factors for distance first, then the conversion factors for time.
#539.0 * color(blue)(cancel(color(black)("m")))/(1color(red)(cancel(color(black)("s")))) * (1color(orange)(cancel(color(black)("km"))))/(10^3color(blue)(cancel(color(black)("m")))) * "1 mi"/(1.609344color(orange)(cancel(color(black)("km")))) * (60color(red)(cancel(color(black)("s"))))/(1color(purple)(cancel(color(black)("min")))) * (60color(purple)(cancel(color(black)("min"))))/"1 hr" = color(darkgreen)(ul(color(black)("1206 mi/hr")))#
The answer is rounded to four sig figs.
Notice that you can also use the four conversion factors to form a single conversion factor that takes you directly from meters per second to miles per hour
#(1color(blue)(cancel(color(black)("m"))))/(1color(red)(cancel(color(black)("s")))) * (1color(orange)(cancel(color(black)("km"))))/(10^3color(blue)(cancel(color(black)("m")))) * "1 mi"/(1.609344color(orange)(cancel(color(black)("km")))) * (60color(red)(cancel(color(black)("s"))))/(1color(purple)(cancel(color(black)("min")))) * (60color(purple)(cancel(color(black)("min"))))/"1 hr" = "2.2369 mi/hr"#
You will once again have
#539.0 color(red)(cancel(color(black)("m/s"))) * "2.2369 mi/hr"/(1color(red)(cancel(color(black)("m/s")))) = color(darkgreen)(ul(color(black)("1206 mi/hr")))#
