Question

our nearest star (other than the sun) is 4.2 light - years away. that is, it takes 4.2 years for the light it emits to reach earth. part a how far away is it in meters? express your answer using two significant figures. d = m

Explanation:

Step1: Calculate the time in seconds

We know that 1 year has 365 days, 1 day has 24 hours, 1 hour has 60 minutes and 1 minute has 60 seconds.
The time \(t = 4.2\) years.
\(t=4.2\times365\times24\times60\times60\) s
\(t = 4.2\times31536000\) s
\(t=1.324512\times 10^{8}\) s

Step2: Use the formula \(d = vt\) (where \(v = c=3\times 10^{8}\) m/s, speed of light)

We substitute \(v = 3\times 10^{8}\) m/s and \(t=1.324512\times 10^{8}\) s into the formula \(d=vt\)
\(d=(3\times 10^{8})\times(1.324512\times 10^{8})\)
Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), we have \(d = 3\times1.324512\times10^{8 + 8}\)
\(d=3.973536\times 10^{16}\) m

Step3: Round to two significant figures

Rounding \(3.973536\times 10^{16}\) to two significant figures, we get \(d = 4.0\times 10^{16}\) m

Answer:

\(4.0\times 10^{16}\) m