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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movies and books is that hibernating astronauts travel far into Earth鈥檚 future, to a time when human civilization has been replaced by an ape civilization. Considering only special relativity, determine how far into Earth鈥檚 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脳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:

鈭�t=t1-vc2

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

Substitute all the values in equation.

鈭�t=120y1-0.9990cc2鈭�t=2.683脳103y

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

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Most popular questions from this chapter

A radar transmitterTisfixedto a reference frame S'that is moving to the right with speed v relative to reference frame S(Fig. 37-33). A mechanical timer (essentially a clock) in frame S', having a period 蟿鈭� (measured inS' ), causes transmitter Tto emit timed radar pulses, which travel at the speed of light and are received by R, a receiver fixed in frame S. (a) What is the period 蟿of the timer as detected by observer A, who is fixed in frame S? (b) Show that at receiver R the time interval between pulses arriving fromT is not 蟿or 蟿o, but

蟿R=蟿oc+vc-v

(c) Explain why receiver Rand observer A, who are in the same reference frame, measure a different period for the transmitter. (Hint: A clock and a radar pulse are not the same thing.)

A meter stick in frame S' makes an angle of 30owith the x鈥� axis. If that frame moves parallel to the x-axis of frame Swith speed 0.90c relative to frame S, what is the length of the stick as measured from S ?

Particle A (with rest energy 200 MeV) is at rest in a lab frame when it decays to particle B (rest energy 100 MeV) and particle C (rest energy 50 MeV). What are the (a) total energy and (b) momentum of B and the (c) total energy and (d) momentum of C?

One cosmic-ray particle approaches Earth along Earth鈥檚 north-south axis with a speed of 0.80ctoward the geographic north pole, and another approaches with a speed of 0.60c toward the geographic south pole (Fig. 37- 34). What is the relative speed of approach of one particle with respect to the other?

Stellar system Q1 moves away from us at a speed of 0.800c. Stellar system Q2, which lies in the same direction in space but is closer to us, moves away from us at speed 0.400c. What multiple of c gives the speed of Q2 as measured by an observer in the reference frame of Q1?
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