Radio communications travel at the speed of light (2.9979×10⁸ meters/sec). How long will it take for a radio transmission to reach a space probe located 1.440×10⁸ miles from earth?

Answer 1

velocity multiplied by time equals distance or v*t = d. We can switch this around since the question want time (how long) so the equation becomes t = d/v

However, we need to adjust for the units. I know that there are 5280 feet in 1 mile and there are 3.2808 feet in 1 meter so distance in meters can be calculated like this:

so that feet cancels feet and miles cancel miles like this:

leaving just meters (which is what we want since velocity is in meters/sec. Now we just have to multiply the numbers. So 1.440×10⁸ times 5280 divided by 3.2808 = 2.3175x10¹¹ meters

Now use the equation t = d/v = 2.3175x10¹¹ / 2.9979×10⁸ = 773.04 seconds. But we need to use the correct number of significant figures. The velocity is given in 5 sig figs and the distance is given in 4 sig figs, so we need to answer to be given in the smaller of these, 4 sig figs. So the answer is 773.0 seconds

Answer 2

This is a straightforward problem in conversions. You are given the speed of light in meters per second. You are given the distance to the space probe in miles. You either have to convert meters to miles or miles to meters. One mile is equal to 1609.344 meters. Doing the conversion,

(1.440 * 10^8 miles) * (1609.344 meters/mile) = 2.317455 * 10^11 meters, expressed in scientific notation.

Dividing the number of meters by the speed of light will give the time

(2.317455 * 10^11 meters) / (2.9979 * 10^8 meters/second) = 7.73026 * 10^2 seconds, expressed in scientific notation.

Since your initial values had five significant figures (for the speed of light) and four significant figures (for the distance) you need to express your answer to four significant figures, so the final answer is

773.0 seconds