Question

c. astronomy the speed of light is $3 \times 10^8$ meters per second. if mars is $2.25 \times 10^{11}$ meters from the sun, how many seconds does it take light to reach mars from the sun? write the answer in scientific notation.

Explanation:

Step1: Recall the formula for time

Time \( t \) is calculated by the formula \( t=\frac{d}{v} \), where \( d \) is distance and \( v \) is velocity. Here, \( d = 2.25\times10^{11}\) meters and \( v=3\times 10^{8}\) meters per second.

Step2: Substitute the values into the formula

\( t=\frac{2.25\times 10^{11}}{3\times 10^{8}} \)

Step3: Divide the coefficients and subtract the exponents of 10

First, divide the coefficients: \( \frac{2.25}{3}=0.75 \). Then, use the rule of exponents \( \frac{10^{m}}{10^{n}}=10^{m - n}\), so \( \frac{10^{11}}{10^{8}}=10^{11-8}=10^{3} \).

Step4: Combine the results

Multiply the coefficient and the power of 10: \( 0.75\times10^{3} \). But in scientific notation, the coefficient should be between 1 and 10. So we rewrite \( 0.75\times 10^{3}\) as \( 7.5\times 10^{2} \) (since \( 0.75\times10^{3}=7.5\times10^{- 1}\times10^{3}=7.5\times10^{2} \)).

Answer:

\( 7.5\times 10^{2} \) seconds