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At time t=0 , in your frame of reference Z, you measure the back of the spaceship to be at x=0 and the front of the ship to be at x=l . Find an equation relating the length that you measure l to the ship's proper length l0 .

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An equation relating the length that you measure l to the ship's proper length l0  is  

l =l0/y. This is further explained below.

What is an equation relating the length that you measure l to the ship's proper length l0?

Generally, Any object's length in a moving frame will look shortened or contracted when seen in that direction. The Lorentz transformation may be used to determine the amount of contraction.

In conclusion, To use the Lorentz Lorentz transformation, the length Lo-x2 - may be determined if it is measured in the moving reference frame. Hence the Resultant l = l0/y.

Read more about Lorentz transformation

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