Question

light travels at approximately 3 x 10^5 miles per second. it takes approximately 5.1 x 10^2 seconds for the light from the sun to reach earth when it is farthest from the sun. based on this information, how far is earth from the sun, in miles, when they are farthest from one another? give your answer in scientific notation and do not include units. provide a coefficient accurate to the nearest hundredth.

Explanation:

Step1: Recall the distance - time formula

Distance \(d = v\times t\), where \(v\) is the speed and \(t\) is the time. The speed of light \(v = 3\times10^{5}\) miles per second and the time \(t=5.1\times 10^{2}\) seconds.

Step2: Calculate the distance

\[

$$\begin{align*} d&=(3\times 10^{5})\times(5.1\times 10^{2})\\ &=(3\times5.1)\times(10^{5 + 2})\\ & = 15.3\times10^{7}\\ &=1.53\times 10^{8} \end{align*}$$

\]

Answer:

\(1.53\times 10^{8}\)