Question

A spacecraft is measured to be 120.0 m long and 20.0 m in diameter while at rest relative to an observer. If this spacecraft now flies by the observer with a speed of 0.99c, what length and diameter does the observer measure?​

Answer 1

Step-by-step explanation:

We can use the Lorentz transformation equations to calculate the length and diameter of the spacecraft as measured by the observer. The equations are:

L' = L/γ

D' = D/γ

where L is the length of the spacecraft at rest, D is the diameter of the spacecraft at rest, γ is the Lorentz factor, and L' and D' are the length and diameter of the spacecraft as measured by the observer.

To calculate γ, we can use the equation:

γ = 1/√(1 - v^2/c^2)

where v is the velocity of the spacecraft relative to the observer (0.99c in this case) and c is the speed of light.

Substituting the given values, we get:

γ = 1/√(1 - 0.99^2) ≈ 7.09

Now, we can calculate the length and diameter as measured by the observer:

L' = L/γ = 120.0 m/7.09 ≈ 16.93 m

D' = D/γ = 20.0 m/7.09 ≈ 2.82 m

Therefore, the observer would measure the length of the spacecraft to be approximately 16.93 m and the diameter to be approximately 2.82 m.