a. the pilot of the spaceship measures the length of the moving ship as 20 meter

Question

a. the pilot of the spaceship measures the length of the moving ship as 20 meters. Determine its length as measure by a person on Earth.

b. The pilot of the spaceship observes that the spaceship travels for 5 years. Determine how much time has passed according to a person on Earth.

c. Some time after passing the Earth, the pilot shoots a laser pulse backward at a speed of 3x10^8 meters per second with respect to the spaceship. Determine the speed of the laser pulse as measure by a person on Earth.

A space ship travels with a constant speed of .8c as it passes by the Earth on its way to a distant star as shown in the diagram above. a. the pilot of the spaceship measures the length of the moving ship as 20 meters. Determine its length as measure by a person on Earth. b. The pilot of the spaceship observes that the spaceship travels for 5 years. Determine how much time has passed according to a person on Earth. c. Some time after passing the Earth, the pilot shoots a laser pulse backward at a speed of 3x10^8 meters per second with respect to the spaceship. Determine the speed of the laser pulse as measure by a person on Earth.

Explanation / Answer

A space ship travels with a constant speed is v = 0.8 c a ) Length of the moving ship is L_s = 20m     length as measure by a person on Earth is L = L_s 1 - v^2 / c^2                                                                       = 20.0 m 1 - (0.8c)^2 / c^2                                                                       = 12.0m The pilot of the space ship observes that the space ship travels for t_0 = 5 years                                                                                                             = 1.5778*10^8 s time passed according to a person on the Earth                                        t = t_0 / 1- v^2 / c^2                                               = 1.5778*10^8 s / 1 - (0.8c)^2 / c^2                                               = 2.629*10^8 s                                              = 8.3 years

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