Question

the fastest human spaceship leaving the solar system is voyager 1, which is travelling at 61,146 km/hr. imagine it is travelling to a star system 8.3 light - years away. calculate how long in years it will take for voyager 1 to arrive.

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Explanation:

Step1: Convert light - years to kilometers

1 light - year is approximately $9.461\times 10^{12}$ km. If the star system is 8.3 light - years away, then the distance $d$ in kilometers is $d = 8.3\times9.461\times 10^{12}$ km.

Step2: Use the formula $t=\frac{d}{v}$

The speed of Voyager 1 is $v = 61146$ km/h. First, convert the speed to km/year. There are $24\times365 = 8760$ hours in a year. So the speed in km/year is $v=61146\times8760$ km/year. Then, $t=\frac{8.3\times9.461\times 10^{12}}{61146\times8760}$.
$8.3\times9.461\times 10^{12}=78.5263\times10^{12}=7.85263\times 10^{13}$
$61146\times8760 = 61146\times(8000 + 700+60)=61146\times8000+61146\times700 + 61146\times60$
$=489168000+42802200+3668760=535638960$
$t=\frac{7.85263\times 10^{13}}{535638960}\approx1.47\times 10^{5}$ years

Answer:

$1.47\times 10^{5}$