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The constant velocity that the spacecraft must travel is : 3.49 * 10⁸ m/s
Given data :
Distance of star from earth = 4.3 light years
Observers time = 3.7 years
Observers time = 3.7 * 365 * 24 * 60 * 60
Distance of star from earth = 4.3 * 9.46 * 10¹⁵
The velocity the spacecraft must travel will be calculated using the equation
V = distance / time
= ( 4.3 * 9.46 * 10¹⁵ ) / ( 3.7 * 365 * 24 * 60 * 60 )
= 3.49 * 10⁸ m/s
Hence we can conclude that The constant velocity that the spacecraft must travel is : 3.49 * 10⁸ m/s
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Attached below is the missing detail related to the question
The constant velocity must the spacecraft travels from the earth will be 3.49×10⁸ m/sec.
The change of distance with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
The given data in the problem is
Distance of earth from stars = 4.3 light year
The given time = 3.7 year
One year converted into the second as;
[tex]\rm 1 \ year = 3.7 \times 365 \ days \ \times 24 \ hour \times 60 \ minute \times 60 \ sec \\\\ 1 year = 116 \times 10^6 \ sec[/tex]
1 light-year into a kilometer as;
[tex]\rm 4.3 \ light year = 4.3 \times 9.46 \times 10^{15 metre} \\\\[/tex]
At what constant velocity must a spacecraft travel from the earth if it is to reach the star in 3. 7 years,
The velocity of the spacecraft's travel from the earth will be;
[tex]\rm V = \frac{d}{t} \\\\ V= \frac{4.3 \times 9.46 \times 10^{15}}{3.7 \times 365 \times 24 \times 60 \times 60 } \\\\\ V= 3.49 \times 10^8 \ m/sec[/tex]
Hence the constant velocity must the spacecraft travels from the earth will be 3.49×10⁸ m/sec.
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