Question

when the curiosity mars rover landed on mars in august 2012, it sent a radio signal with the message, \it once was a small step ... now its six big wheels.\ the distance between mars and earth on landing day was 248,000,000 km. at the speed of light (299,000 km/s) how long, in minutes, did it take the message to travel to earth? (a) in the boxes, enter the distance between mars and earth and the speed of light in scientific notation. distance between mars and earth: ×10 km speed of light: ×10 km/s

Explanation:

Step1: Convert distance to scientific - notation

To convert 248,000,000 km to scientific notation, move the decimal point 8 places to the left. So, $248000000 = 2.48\times10^{8}$ km.

Step2: Convert speed of light to scientific - notation

To convert 299,000 km/s to scientific notation, move the decimal point 5 places to the left. So, $299000=2.99\times 10^{5}$ km/s.

Step3: Calculate time in seconds

We know that time $t=\frac{d}{v}$, where $d$ is distance and $v$ is speed. Substituting $d = 2.48\times10^{8}$ km and $v = 2.99\times 10^{5}$ km/s, we get $t=\frac{2.48\times 10^{8}}{2.99\times 10^{5}}=\frac{2.48}{2.99}\times10^{8 - 5}\approx0.83\times10^{3}=830$ s.

Step4: Convert time from seconds to minutes

Since 1 minute = 60 seconds, then the time in minutes is $\frac{830}{60}=\frac{83}{6}\approx13.83$ minutes.

Answer:

Distance between Mars and Earth: $2.48\times 10^{8}$ km
Speed of light: $2.99\times 10^{5}$ km/s
Time taken for the message to travel to Earth: approximately 13.83 minutes.