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Mathematics 16 Online
zarkam21:

A goose is flying south for the winter at a constant speed. Keep in mind that one mile is 1.61 km and one pound is 454 g. The goose has a mass of 23.9 lb (pounds) and is flying at 8.00 miles/h (miles per hour). What is the kinetic energy of the goose in joules?

zarkam21:

I got 900026.8883 J

Vocaloid:

hm, probably not, that's a lot of energy for one bird

Vocaloid:

anyway, this is a very complicated conversion factor but let's start w/ 8.0 mph|dw:1536695159208:dw|

zarkam21:

ok

Vocaloid:

1 mile = 1.61 km as indicated by the problem so let's put that where it belongs so the units can cancel out

zarkam21:

okay so it would be 1.61/1mile

Vocaloid:

|dw:1536695216132:dw|

Vocaloid:

60 minutes in an hour, 60 seconds in a minute so applying these conversion factors:

Vocaloid:

|dw:1536695254643:dw|

Vocaloid:

|dw:1536695274189:dw|

zarkam21:

Where do you 1 hr/60 min and 1min/60s conversions come into play. Like why are those there?

zarkam21:

I'm sorry Im really trying to understand so thats why I ask questions

Vocaloid:

the units of joules are kg * (m/s^2) so we need to convert from hours to seconds

zarkam21:

ohh because we havew to have seconds

zarkam21:

okay i understand

Vocaloid:

oh, I forgot, we need to convert from km to meters but that's just a simple 1000 * multiplication

Vocaloid:

|dw:1536695401195:dw|

Vocaloid:

anyway multiplying all that out gives us 8 * 1.61 * 1000 / (60*60) = 3.57777....cont. m/s

Vocaloid:

now, since units of joules need kg not pounds we do another conversion to get 23.9 lb to kg

Vocaloid:

|dw:1536695508275:dw|

Vocaloid:

multiplying all that out gives (23.9/1000)*454 = 10.8506kg

Vocaloid:

thankfully it's the easy part now 1/2 mv^2 = (1/2)(10.8506)( 3.57777)^2

zarkam21:

are you dividing it by 1000 because you want it to go from grams to kilograms?

Vocaloid:

yes

zarkam21:

69.44621722

Vocaloid:

yup and since we have three sig figs we round that to 69.4

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