Question

radio waves travel at the speed of light, which is $3.00 \times 10^8$ m/s. how many minutes does it take for a radio message to reach earth from saturn if saturn is $7.9 \times 10^8$ km from earth?\
\\(\circ 4.4 \times 10^{-2}\\) min\
\\(\circ 1.6 \times 10^5\\) min\
\\(\circ 4.0 \times 10^{15}\\) min\
\\(\circ 44\\) min\
\\(\circ 2.6\\) min

Explanation:

Step1: Convert distance to meters

The distance from Saturn to Earth is \(7.9\times 10^{8}\) km. Since \(1\) km \( = 1000\) m \(= 10^{3}\) m, we convert the distance to meters:
\(d = 7.9\times 10^{8}\text{ km}\times10^{3}\text{ m/km}=7.9\times 10^{11}\text{ m}\)

Step2: Use the formula \(t=\frac{d}{v}\) to find time in seconds

The speed of light (radio waves) \(v = 3.00\times 10^{8}\text{ m/s}\). Using the formula \(t=\frac{d}{v}\), we substitute the values:
\(t=\frac{7.9\times 10^{11}\text{ m}}{3.00\times 10^{8}\text{ m/s}}\approx2.633\times 10^{3}\text{ s}\)

Step3: Convert seconds to minutes

Since \(1\) minute \( = 60\) seconds, we convert the time from seconds to minutes:
\(t=\frac{2.633\times 10^{3}\text{ s}}{60\text{ s/min}}\approx44\text{ min}\)

Answer:

44 min