2026-09-10T00:15:02.274280 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL Use the information below and the diagram to answ...
Question 1 Report
Use the information below and the diagram to answer parts (a) and (b).
A star is \(6.3 \times 10^{14}\) km from Earth, and light travels at \(3.0 \times 10^{5}\) km per second.
(a) Calculate the time light takes to travel from the star to Earth. Give your answer in seconds, in standard form. [3]
(b) One year is \(3.15 \times 10^{7}\) seconds. Work out this time in years, to the nearest year. [2]
Answer Details
(a) The time is found from \(\text{time}=\text{distance}\div\text{speed}\).
\[\text{time}=\frac{6.3\times10^{14}}{3.0\times10^5}\]
Divide the coefficients and subtract the powers of ten:
\[\frac{6.3}{3.0}=2.1,\qquad\frac{10^{14}}{10^5}=10^{14-5}=10^9\]
\[\text{time}=\boxed{2.1\times10^9\text{ s}}\]
[M1 M1 A1]
(b) Convert seconds to years by dividing by the number of seconds in one year:
\[\text{years}=\frac{2.1\times10^9}{3.15\times10^7}=66.66\ldots\]
To the nearest year, the time is \(67\) years. [M1 A1]
For division in standard form, subtract exponents. The answer to part (a) is already in standard form because \(2.1\) is between \(1\) and \(10\).
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