QuestionConvert a speed of $1.07928 \times 10^{9}$ m/s to miles per minute (mi/min).

Studdy Solution

STEP 1

Assumptions1. The given speed is $1.07928 \times10^{9}$ m/s. We need to convert this speed to miles per minute (mi/min)
3. We know the following conversion factors -1 mile =1609.34 meters -1 minute =60 seconds

STEP 2

First, we need to convert the speed from meters per second (m/s) to miles per second (mi/s). We can do this by dividing the given speed by the conversion factor for meters to miles.
$Speed_{mi/s} = Speed_{m/s} / Conversion\, factor_{m\, to\, mi}$

STEP 3

Now, plug in the given values for the speed and the conversion factor to calculate the speed in miles per second.
$Speed_{mi/s} =1.07928 \times10^{9}\, m/s /1609.34\, m/mi$

STEP 4

Calculate the speed in miles per second.
$Speed_{mi/s} =1.07928 \times10^{9}\, m/s /1609.34\, m/mi =670616.627\, mi/s$

STEP 5

Now that we have the speed in miles per second, we need to convert this to miles per minute. We can do this by multiplying the speed in miles per second by the conversion factor for seconds to minutes.
$Speed_{mi/min} = Speed_{mi/s} \times Conversion\, factor_{s\, to\, min}$

STEP 6

Plug in the values for the speed and the conversion factor to calculate the speed in miles per minute.
$Speed_{mi/min} =670616.627\, mi/s \times60\, s/min$

STEP 7

Calculate the speed in miles per minute.
$Speed_{mi/min} =670616.627\, mi/s \times60\, s/min =40236996.62\, mi/min$ The speed is approximately $4.023699662 \times10^{7}$ miles per minute.

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