Question

A ladder 5.0 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 3.0 m from the wall, and the top of the ladder is 4.0 m above the floor. The spaceship moves past the Earth with a speed of 0.90c in a direction parallel to the floor of the ship. Find the angle the ladder makes with the floor as seen by an observer on Earth

Answer 1

the angle the ladder makes with the floor as seen by an observer on Earth is 71.9°

Step-by-step explanation:

Given the data in the question and as illustrated in the diagram below.

speed of the ship v = 0.90c

base of the ladder from the wall x₀ = 3.0 m

top of the later above the floor y = 4.0 m

we determine angle θ.

from the diagram,

tanθ = y/x₀

tanθ = y / x₀√( 1 - v²/c² )

we substitute

tanθ = 4.0 / 3.0√( 1 - ((0.9c)²/c²) )

tanθ = 4.0 / 3.0√( 1 - ((0.9²)c²/c²) )

tanθ = 4.0 / 3.0√( 1 - (0.9²) )

tanθ = 4.0 / 3.0√( 1 - 0.81 )

tanθ = 4.0 / 3.0√0.19

tanθ = 4.0 / 1.30766968

tanθ = 3.058876

θ = tan⁻¹( 3.058876 )

θ = 71.8965 ≈ 71.9°

Therefore, the angle the ladder makes with the floor as seen by an observer on Earth is 71.9°