4) A ladder 5.60 m long leans against a wall inside a spaceship. From the point

Question

4) A ladder 5.60 m long leans against a wall inside a spaceship. From the point of view of a person on the ship, the top of the ladder is 4.85 m above the floor. The spaceship moves past the Earth with a speed of 0.82c in a direction parallel to the floor of the ship. What is the length of the ladder as seen by an observer on Earth?

5) A person on earth notices a rocket approaching from the right at a speed of 0.78c and another rocket approaching from the left at 0.56c. What is the relative speed between the two rockets, as measured by a passenger on one of them?

Explanation / Answer

4.  height h = [5.6^2-4.85^2 ]= 2.8 m

tan = h/l = h/ (l'*[1-(v/c)^2] = 2.8/( 4.85*[1-(0.82)^2]

= 72.64º

5. In relativity, the frame of each of the rockets has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed and can also be called the composition law for velocities. For collinear motions, the velocity of one rocket wrt the passenger on another rocket is given by: S=(U+V)/(1+(V/c)(U/c)) = (.56+.78)c/(1+.56*.78) = .932c.

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