Answer to Question #183079 in Mechanics | Relativity for mary

Question #183079

Two inertial systems are uniformly separating at a speed of exactly √0.84𝑐. In one system a jogger runs a mile (1609m) 

in 6 min along the axis of relative motion. How far in meters does he run and how long does it take, to observers in the other 

system?


1
Expert's answer
2021-04-22T07:34:35-0400

To be given in question

Velocity (v)=√(0.84c)

L0=1609meterL_{0}=1609 meter

Z0Z_{0} = 6 minutes

To be asked in question

Distance run=?

Times run=?

We know that

L=L01βˆ’v2c2β†’(1)L=L_{0}\sqrt{1-\frac{v^2}{c^2}}\rightarrow(1)

Z=Z01βˆ’v2c2β†’(2)Z=\frac{Z_{0}}{\sqrt{1-\frac{v^2}{c^2}}}\rightarrow(2)

Eqution (1) put valuesL=1609Γ—1βˆ’.84c2c2L=1609\times\sqrt{1-\frac{\sqrt{.84c}^2}{c^2}}

L=1609Γ—.16L=1609\times\sqrt{.16}

L=1609Γ—0.4L=1609\times0.4

L=643.6meterL=643.6meter

Time

Eqution (2)put values

Z=3601βˆ’v2c2Z= \frac{360}{\sqrt{1-\frac{v^2}{c^2}}}

Put v=√(.84c)

Z=3600.4Z=\frac{360}{0.4}

Z=900 sec

Z=90060Z=\frac{900}{60} =15 minutes

Z=15minutes after and distance L=643.6meter after observer is other systems βˆ†d=1609βˆ’643.9βˆ†d=1609-643.9

Separation of speed =

distancetime→equation(1)\frac{distance}{time}\rightarrow equation (1)


Put values

Speed=965.1900=1.07mete/secSpeed=\frac{965.1}{900}=1.07mete/sec

SpeedSpeed separation of distance βˆ†d=d1βˆ’d2β†’(2)βˆ†d=d_{1}-d_{2}\rightarrow(2)

Put valuesd1=1609meter

d2=643.6meter equation (2) put values

βˆ†d=965.1meter

Separation distance 965.1meter

Separation Speed=1.072meter/sec



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