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**1. Homework Statement**

A jetliner touches down at 270 km/h. The plane then decelerates (i.e., undergoes acceleration directed opposite its velocity) at 4.5 m/s2. What’s the minimum runway length on which this aircraft can land?

**2. Homework Equations**

v

^{2}

_{fx}= v

^{2}

_{ix}+ 2a

_{x}Δ

_{x}

**3. The Attempt at a Solution**

i got the solution doing this:

(270km/hr)(1000m/km)(hr/3600s) = 75m/s

0 = (75m/s)

^{2}+ 2(-4.5m/s

^{2})Δ

_{x}

(-9m/s)Δ

_{x}= 5625m

^{2}/s

^{2}

Δ

_{x}= 625m

which is the correct answer.

however, i also tried to get the answer by converting everything to km/h, and i couldn't get the correct answer. i can't figure out why, and it's driving me crazy. here's what i tried:

0 = (270km/hr)

^{2}+ 2(-4.5 m/s

^{2})Δ

_{x}

9m/s

^{2}Δ

_{x}= 72900km

^{2}/hr

^{2}

and then an aside for unit conversion:

(9m/s

^{2})(km/1000m)(3600s

^{2}/hr

^{2}) = 32.4km/hr

^{2}

i plugged that in to get

32.4km/hr

^{2}Δ

_{x}= 72900km

^{2}/hr

^{2}

Δ

_{x}= 2250 km, which is much, much more than the 625 m that i got above.

what am i doing wrong?!?

thanks for the help, i really appreciate it

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