physics Two spaceships approach Earth with equal speeds (es viewed from Earthi b

Question

physics

Two spaceships approach Earth with equal speeds (es viewed from Earthi but from oppostedirections. A standard 1m stick is measured to be 40amlong bw an occupant of the other spaceship what is the speed of the each spaceship, as measured by the Earth obserwer? Problem 2 A beam of muons travels through the lab with speed 0.Bc. Assuming 2.2 microsecond restframe lifetime of muons what is the mean distance traveled by muons? instead of standard laboratory o emt a hydrogen li (Balmerl ine at 580nm A distant galaxy is What is its approximate speed? value of 43Anm. Is the galaxy receding or approaching? Problem 4: star, 4 light years away, A woman leaves the Earth in a spacecraft that makes a roundtrip to the neare who at a speed 09. How much younger is she upon her return than her twin sister remained of

Explanation / Answer

1) The length of the meter stick in the frame of the observer L = 1 m / gamma

gamma = 1 m / 0.4 = 2.5

gamma = 1 / sqrt [1 - beta2]

sqrt [1 - beta2] = 1 / 2.5

1 - beta= 0.16

beta = 0.92 c

if v is the speed of spacecraft 1 in the frame of reference of the Earth then Ux = v

Ux' = -0.92 c

Ux' = ux - v / [1 - v ux'/c2]

-0.92 c = -v - v / [1 - v[-v]/c2]

0.92 = 2 beta / 1 - beta2

0.92 beta2 - 2 beta + 0.92 = 0

beta = 0.66 c

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