physics homework

Question

A small turtle moves at a speed of 651 furlongs per fortnight. Find the speed of the turtle in centimeters per second. Note that 1 furlong = 220 yards and 1 fortnight = 14 days.

Answer 1

You can use dimensional or unit analysis by setting up a "daisy chain" of conversion factors such that the intermediate units cancel out, leaving the ones you want. In this case you start with fl/fn and end with cm/sec.

651fl/fn x 1 fn/14 days x 1day/24 hrs x 1 hr/60 min x 1 min/60 sec x 220 yds/1 fl x 3 ft/1 yd x 12 in/1 ft x 2.54 cm/in. The result of the multiplication is 10.83 cm/sec.

Answer 2

Hi,

This problem is going to be all about conversions. You know that the speed that you were given was 651 furlongs/fortnight and we want it in cm/s. So that means that we need to convert furlongs into cm and fortnights into seconds, then divide those two conversions by each other to get our conversion to cm/s.

furlongs to cm: The problem tells us that 1 furlong = 220 yards. 1 yard = 3 feet, so 220 yards = 660 feet. 1 foot = 12 inches, so 660 feet = 660x12 = 7920 inches. Now we can finally get to cm, because the inch is defined to be exactly 2.54 cm. Therefore, 1 inch = 2.54 cm and we can write 7920 inches = 7920x2.54 = 20116.8 cm

fortnight to s: Now we have to convert between fortnights to seconds. The problem states that 1 fortnight = 14 days. 1 day = 24 hours, so 14 days = 14x24 = 336 hours. 1 hour = 60 minutes, so 336 hours = 336x60 = 20160 minutes. Finally, every minute is 60 seconds so 20160 minutes = 20160x60 = 1209600 seconds

furlong/fortnight to cm/s: Now we can divide these two figures by one another to get the conversion from furlong/fortnight to cm/s and get our final result. 1 furlong = 20116.8 cm and 1 fortnight = 1209600 s. So, 1 furlong/fortnight = 20116.8 cm/ 1209600 s = 0.0166 cm/s. Therefore, 651 furlongs/fortnight = 651x0.0166 = 10.81 cm/s, which is the result that you were looking for.