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Chapter 37: Q7P (page 1145)


The premise of the Planet of the Apes movies and books is that hibernating astronauts travel far into Earth’s future, to a time when human civilization has been replaced by an ape civilization. Considering only special relativity, determine how far into Earth’s future the astronauts would travel if they slept for 120 y while traveling relative to Earth with a speed of 0.9990c, first outward from Earth and then back again?

Short Answer

Expert verified

The duration for future travel by astronaut is 2.683×103y.

Step by step solution

01

Identification of given data

The speed of astronauts relative to Earth is v=0.9990c

The duration of the sleep of an astronaut is t=120y

The time dilation is used to find the duration of particles before decaying from the detector.

02

Determination of duration for future travel by astronaut

The duration for future travel by astronaut is given as:

∆t=t1-vc2

Here, is the speed of light and its value is 3×108m/s .

Substitute all the values in equation.

∆t=120y1-0.9990cc2∆t=2.683×103y

Therefore, the duration for future travel by astronaut is 2.683×103y.

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Most popular questions from this chapter

In Fig. 37-35, three spaceships are in a chase. Relative to an x-axis in an inertial frame (say, Earth frame), their velocities are vA=0.900c, vB, and vc=0.900c. (a) What value of vBis required such that ships A and C approach ship B with the same speed relative to ship B, and (b) what is that relative speed?

In a high-energy collision between a cosmic-ray particle and a particle near the top of Earth’s atmosphere, 120 km above sea level, a pion is created. The pion has a total energy E of 1.35×105MeVand is travelling vertically downward. In the pion’s rest frame, the pion decays 35.0 ns after its creation. At what altitude above sea level, as measured from Earth’s reference frame, does the decay occur? The rest energy of a pion is 139.6 MeV.

Figure 37-16 shows a ship (attached to reference frame S') passing us (standing in reference frame S) with velocity v→=0.950ci^. A proton is fired at speed 0.980c relative to the ship from the front of the ship to the rear. The proper length of the ship is 760 m . What is the temporal separation between the time the proton is fired and the time it hits the rear wall of the ship according to (a) a passenger in the ship and (b) us? Suppose that, instead, the proton is fired from the rear to the front. What then is the temporal separation between the time it is fired and the time it hits the front wall according to (c) the passenger and (d) us?

A pion is created in the higher reaches of Earth’s atmosphere when an incoming high-energy cosmic-ray particle collides with an atomic nucleus. A pion so formed descends toward Earth with a speed of 0.99c. In a reference frame in which they are at rest, pion decay with an average life of 26 ns. As measured in a frame fixed with respect to Earth, how far (on the average) will such a pion move through the atmosphere before it decays?

The length of a spaceship is measured to be exactly half its rest length. (a) To three significant figures, what is the speed parameter βof the spaceship relative to the observer’s frame? (b) By what factor do the spaceship’s clocks run slow relative to clocks in the observer’s frame?
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