Respuesta :
Answer:
The angle made by the ladder on the floor, [tex]\theta = 74.52^{\circ}[/tex]
Given:
Length of the ladder, l = 5.10 m
Base of the ladder from the wall, [tex]L_{o} = 2.50 m[/tex]
Top of the ladder, [tex]H_{o} = 4.45 m[/tex]
Speed of the spaceship, [tex]v_{s} = 0.87c[/tex]
Explanation:
Now, using the formula for length contraction from Einstein's theory of relativity:
[tex]L = L_{o}\sqrt{\frac{1 - v_{s}^{2}}{c^{2}}}[/tex]
where
c = speed of light in vacuum
From the above relation for length contraction:
[tex]L = 2.5\sqrt{\frac{1 - (0.87c)^{2}}{c^{2}}}[/tex]
L = 1.233 m
Now, the angle made by the ladder on the floor:
[tex]tan\theta = \frac{H_{o}}{L}[/tex]
[tex]\theta = tan^{- 1}\frac{4.45}{1.233}[/tex]
[tex]\theta = 74.52^{\circ}[/tex]
