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Solving for Speed

1 - A swimmer wants to swim straight across a river with current flowing at a speed of v1 = 0.27 km/h. If the swimmer swims in still water with speed v2 = 0.81 km/h, at what angle should the swimmer point upstream from the shore and at what speed v will the swimmer swim across the river?

2 - In the 1887 experiment by Michelson and Morley, the length of each arm was 11 m. The experimental limit for the fringe shift was 0.005 fringes. If sodium light was used with the interferometer ( = 589 nm), what upper limit did the null experiment place on the speed of the Earth through the expected ether?

3 - Astronomers discover a planet orbiting around a star similar to our sun that is 15 light years away. How fast must a rocket ship go if the round trip is to take no longer than 30 years in time for the astronauts aboard?
How long will the trip take as measured on Earth?

4 - A spaceship is moving at a speed ot 0.7c away from an observer at rest. A boy in the spaceship shoots a proton gun with protons having a speed of 0.8c.
(a) What is the speed of the protons measured by the observer at rest when the gun is shot away from the observer?
(b) What is the speed of the protons measured by the observer at rest when the gun is shot toward the observer?

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This solution provides equations with diagrams for various questions solving for speed.

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