Question

A ladder 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, and the top of the ladder is 5.01 m above the floor. The spaceship moves past the Earth with a speed of 0.89c in a direction parallel to the floor of the ship. What is the length of the ladder as seen by an observer on Earth?

Answer 1

From the formula of length contraction we have

$\Delta L = L_0\sqrt{1 - \frac{v^2}{c^2}}$

$\Delta L = 2.5\sqrt{1 - 0.89^2}$

$\Delta L = 1.14 m$

Final length observed is given by

$H = \sqrt{1.14^2 + 5.01^2 } = 5.14 m$