# Calculating Length of Ship B in Frame Ref A

• shyguy79
In summary, to calculate the length of Ship B in Frame Ref A, you will need to measure the distance between two points on the ship's hull - one at the bow and one at the stern. This requires tools such as a measuring tape, ruler, and level. It is not possible to accurately calculate the length without physically measuring the ship, and any unit of length can be used as long as it is consistent throughout the calculation. Calculating the length is important for ship design, construction, and maintenance, as well as determining stability, load capacity, and maneuverability.
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?

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.

## 1. How do you calculate the length of Ship B in Frame Ref A?

To calculate the length of Ship B in Frame Ref A, you will need to measure the distance between two points on the ship's hull. One point should be at the bow (front) of the ship and the other at the stern (back) of the ship. This distance is the length of Ship B in Frame Ref A.

## 2. What tools are needed to calculate the length of Ship B in Frame Ref A?

To accurately measure the length of Ship B in Frame Ref A, you will need a measuring tape or ruler, a pencil, and a paper to record your measurements. You may also need a level to ensure accuracy.

## 3. Can the length of Ship B in Frame Ref A be calculated without physically measuring the ship?

No, the length of Ship B in Frame Ref A cannot be accurately calculated without physically measuring the ship. Visual estimations or using previous measurements of the ship will not provide an accurate result.

## 4. Are there any specific units of measurement that should be used when calculating the length of Ship B in Frame Ref A?

The length of Ship B in Frame Ref A can be measured in any unit of length, such as feet, meters, or centimeters. However, it is important to use the same units consistently throughout the calculation for accurate results.

## 5. Why is it important to calculate the length of Ship B in Frame Ref A?

Calculating the length of Ship B in Frame Ref A is important for various reasons. It provides valuable information for ship design, construction, and maintenance. It is also necessary for determining the ship's stability, load capacity, and maneuverability. Accurate length measurements are crucial for ensuring the safety and efficiency of the ship.

• Introductory Physics Homework Help
Replies
44
Views
911
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
27
Views
417
• Introductory Physics Homework Help
Replies
15
Views
557
• Introductory Physics Homework Help
Replies
2
Views
959
• Introductory Physics Homework Help
Replies
6
Views
990
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
12
Views
2K