Question

11. One light year is the distance light travels in one year, which is 9.461*1015m.The nearest star to Earth is Alpha Centauri, which is 4.35 light years away. Calculatethe distance in:a. mb. kmc. milesd. How long would it take to get there flying on a jumbo jet at 400mph?

Answer 1

Part A. We are given the distance that light travels in one year. To determine the distance equivalent to 4.35 light-years we need to use the following relationship:

$4.35\text{ light years}\times\frac{9.461\times10^{15}m}{1light\text{ year}}$

Solving the operations we get:

$4.35\text{ light years=4.12}\times10^{16}m$

Part B. To convert this distance into kilometers we will use the following conversion factor:

$1km=1000m$

Using the conversion factor we get:

$4.12\times10^{16}m\times\frac{1\operatorname{km}}{1000m}=4.12\times10^{13}\operatorname{km}$

Part C. To convert the distance into miles we will use the following conversion factor

$1mile=1.6\operatorname{km}$

using the conversion factor:

$4.12\times10^{13}\operatorname{km}\times\frac{1mile}{1.6\operatorname{km}}=2.57\times10^{16}miles$

Part D. Given the velocity we can determine time using the following equation:

$t=\frac{d}{v}$

Where "t" is time, "d" is distance and "v" is velocity. Replacing the values we get:

$t=\frac{2.57\times10^{16}miles}{400\text{ miles/h}}$

Solving the operation we get:

$t=6.43\times10^{13}hours$