Question #226426

A ladder 7.00 m long leans against a wall inside a spaceship. From the point of view of a person on the ship, the base of the ladder is 2.50 m from the wall. The spaceship moves past the Earth with a speed of 0.94c in a direction parallel to the floor of the ship. What is the length of the ladder as seen by an observer on Earth?


1
Expert's answer
2021-08-16T08:36:15-0400

Given:

l=7.00ml=7.00\:\rm m

lx=2.50ml_x=2.50\:\rm m


We have

ly=l2lx2=7.0022.502=6.54ml_y=\sqrt{l^2-l_x^2}=\sqrt{7.00^2-2.50^2}=6.54\:\rm m

The Lorentz transformations give

lx=lx1v2/c2=2.5010.942=0.853ml_x'=l_x\sqrt{1-v^2/c^2}=2.50\sqrt{1-0.94^2}=0.853\:\rm mly=ly=6.54ml_y'=l_y=6.54\:\rm m

Hence, the length of the ladder as seen by an observer on Earth

l=lx2+ly2=0.8532+6.542=6.59ml'=\sqrt{l_x'^2+l_y'^2}=\sqrt{0.853^2+6.54^2}=6.59\:\rm m

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