Question

the approximate distance between mars and earth is about 1.32 × 10^8 miles. how many seconds would it take for tv pictures transmitted from the viking space vehicle on marss surface to reach earth? round your answer to 3 significant digits. (1609 m = 1 mi) note: reference the fundamental constants table for additional information.

Explanation:

Step1: Convert miles to meters

Given distance \(d = 1.32\times10^{8}\text{ mi}\). Since \(1\text{ mi}=1609\text{ m}\), then \(d=(1.32\times 10^{8})\times1609\text{ m}\).

$$d = 1.32\times1609\times10^{8}\text{ m}=2.12388\times 10^{11}\text{ m}$$

Step2: Use the speed - distance formula \(t=\frac{d}{v}\)

The speed of light \(v = 3\times10^{8}\text{ m/s}\). Substitute \(d = 2.12388\times 10^{11}\text{ m}\) and \(v = 3\times10^{8}\text{ m/s}\) into \(t=\frac{d}{v}\).

$$t=\frac{2.12388\times 10^{11}}{3\times 10^{8}}\text{ s}$$

Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\) (\(a
eq0\)), we have \(t=\frac{2.12388}{3}\times10^{11-8}\text{ s}\)

$$t = 0.70796\times10^{3}\text{ s}=708\text{ s}$$

Answer:

\(708\) seconds