Question

How many minutes does it take light from the sun to reach Earth, given that the distance from the sun to Earth is 93 million mi, and the speed of light is 3.00 x 10^8 m/s

These types of questions are hard for me. Please explain how to set up the best you can.

Answer 1

this is a conversion problem, more than anything. You have some base information, in this case, a distance and a speed. You're looking for a \(time\). The units of speed are a \(ratio\) of units that you can use as a conversion fraction. In general:
\[speed = \frac{distance}{time}\]so\[time = \frac{distance}{speed}\]This problem is a little more complicated, because it's asking you for \(minutes\), but gives you information in \(seconds\). So there's another step involved. You can't just take the given distance and the given speed and divide them, because:\[\frac{9.3*10^7miles}{3*10^8\frac{m}{s}}\] doesn't properly cancel the units of \(distance\). One meter is NOT equivalent to one mile. You have to change one of those units to match the other. Algebraically it doesn't matter which one, but we use metric measurements in science, so I'm going to get rid of the miles.

Since \[1 mile = 1609m\] then \[9.3*10^7 \cancel{miles}*\frac{1609m}{1 \cancel{mile}} = 1.49*10^{11}m\]

NOW you can divide the distance by the speed because the UNITS cancel properly. Most of your conversion problems are tackled the exact same kind of way

Answer 2

okay so then how technically would you divide those. just work out each in scientific notation to standard and then divide?

Answer 3

so the answer would be 1.602 x 10^3?

Answer 4

but that is not one of my answer choices. the choices are A. 500min B. 0.517min C. 8.3min D. 8.26

Answer 5

what UNIT comes after that \(1.602*10^3\)?

Answer 6

meters?

Answer 7

you just cancelled the meters. You're looking for a measurement of TIME. Check the problem for the unit of time

Answer 8

Seconds?

Answer 9

it's in seconds.

Answer 10

so how do you change seconds into minutes?

Answer 11

times by 60?

Answer 12

if you take 60 seconds and multiply by 60, does that turn it into minutes?

Answer 13

no, then you would divide.

Answer 14

\[1 minute = 60 seconds\]so\[1.602*10^3 \cancel{seconds} * \frac{1 minute}{60 \cancel{seconds}}\]

Answer 15

to get really good at conversion problems, you should start looking at the UNITS as being more important than the numbers

Answer 16

but that still gives me 26.70250897 in my calculator

Answer 17

then your original 1.602*10^3 is incorrect