Calculating Length of Ship B in Frame Ref A

[shyguy79]

Homework Statement

-------------->Va Vb<---------------
FRAME REF A FRAME REF B

-------------------------------------------- Stationary frame ref C

An observer using the frame Ref A, calculate the length of ship B and the time it takes for the whole of ship B to pass by the whole of ship A. Answer as a multiple of ΔtA.

Homework Equations

$\gamma=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$
$L_{0}=\gamma L$
$\delta T=\gamma\delta T_{0}$

The Attempt at a Solution

I think that $\frac{L_{A}}{\gamma}=L_{C}$ but this is where I'm stuck... how do I find the time using what little i have?

 

[anathema]

First, let's define the variables we will be using:
L_A = length of ship A in frame Ref A
L_B = length of ship B in frame Ref B
v = velocity of ship B relative to frame Ref A and Ref B
c = speed of light
γ = Lorentz factor
Δt_A = time interval in frame Ref A

To find the length of ship B in frame Ref B, we can use the equation L_B = γL_A, where γ = 1/√(1-v^2/c^2). This gives us the length of ship B in terms of ship A's length in frame Ref A.

To find the time it takes for the whole of ship B to pass by the whole of ship A, we can use the time dilation equation Δt_B = γΔt_A, where Δt_B is the time interval in frame Ref B. This gives us the time in frame Ref B in terms of the time interval in frame Ref A.

To answer the question as a multiple of Δt_A, we can divide both equations by Δt_A to get L_B/Δt_A = (γL_A)/Δt_A and Δt_B/Δt_A = γ. This means that the length of ship B in frame Ref B is a multiple of the length of ship A in frame Ref A, and the time interval in frame Ref B is a multiple of the time interval in frame Ref A.

In summary, the length of ship B in frame Ref B is γ times the length of ship A in frame Ref A, and the time interval in frame Ref B is also γ times the time interval in frame Ref A. Therefore, the answer to the question is that the length of ship B is γ times the length of ship A, and the time it takes for the whole of ship B to pass by the whole of ship A is also γ times the time interval in frame Ref A.