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Answer :
Final answer:
The relativistic mass of the space vehicle is approximately 259,800 kg.
Explanation:
To determine the relativistic mass of the space vehicle, we can use the formula for relativistic mass:
m = γ * m0
Where m is the relativistic mass, γ is the Lorentz factor, and m0 is the rest mass. The Lorentz factor can be calculated using the formula:
γ = 1 / sqrt(1 - (v^2 / c^2))
Where v is the speed of the space vehicle and c is the speed of light. Plugging in the given values, we get:
v = 2.6 x 10^8 m/s
c = 3 x 10^8 m/s
m0 = 150,000 kg
Calculating γ:
γ = 1 / sqrt(1 - ((2.6 x 10^8)^2 / (3 x 10^8)^2))
γ ≈ 1.732
Now, calculating the relativistic mass:
m = γ * m0
m ≈ 1.732 * 150,000 kg ≈ 259,800 kg
Therefore, the relativistic mass of the space vehicle is approximately 259,800 kg.
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