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QuestionConvert 64ft/s64 \mathrm{ft/s} to cm/min\mathrm{cm/min} and express your answer in scientific notation.

Studdy Solution

STEP 1

Assumptions1. The given speed is 64ft/s64 \mathrm{ft} / \mathrm{s} . We need to convert this speed to cm/min\mathrm{cm} / \mathrm{min}
3. We know that1 foot =30.48 cm and1 minute =60 seconds

STEP 2

First, we need to convert the speed from feet per second to centimeters per second. We can do this by multiplying the given speed by the conversion factor for feet to centimeters.
Speedcm/s=Speedft/stimesConversion factorft to cmSpeed_{cm/s} = Speed_{ft/s} \\times Conversion\, factor_{ft\, to\, cm}

STEP 3

Now, plug in the given values for the speed and the conversion factor to calculate the speed in centimeters per second.
Speedcm/s=64ft/stimes30.48cm/ftSpeed_{cm/s} =64 \mathrm{ft/s} \\times30.48 \mathrm{cm/ft}

STEP 4

Calculate the speed in centimeters per second.
Speedcm/s=64ft/stimes30.48cm/ft=1950.72cm/sSpeed_{cm/s} =64 \mathrm{ft/s} \\times30.48 \mathrm{cm/ft} =1950.72 \mathrm{cm/s}

STEP 5

Next, we need to convert the speed from centimeters per second to centimeters per minute. We can do this by multiplying the speed in centimeters per second by the conversion factor for seconds to minutes.
Speedcm/min=Speedcm/stimesConversion factors to minSpeed_{cm/min} = Speed_{cm/s} \\times Conversion\, factor_{s\, to\, min}

STEP 6

Now, plug in the values for the speed in centimeters per second and the conversion factor to calculate the speed in centimeters per minute.
Speedcm/min=1950.72cm/stimes60s/minSpeed_{cm/min} =1950.72 \mathrm{cm/s} \\times60 \mathrm{s/min}

STEP 7

Calculate the speed in centimeters per minute.
Speedcm/min=1950.72cm/stimes60s/min=117043.2cm/minSpeed_{cm/min} =1950.72 \mathrm{cm/s} \\times60 \mathrm{s/min} =117043.2 \mathrm{cm/min}

STEP 8

Finally, we need to express the speed in scientific notation. We can do this by moving the decimal point two places to the left and multiplying by 10210^2.
Speedcm/min=1.170432times105cm/minSpeed_{cm/min} =1.170432 \\times10^5 \mathrm{cm/min}The speed is 1.170432times105cm/min1.170432 \\times10^5 \mathrm{cm/min}.

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