please answer all questions, i am not sure if my answesr are right Two cars are

Question

please answer all questions, i am not sure if my answesr are right

Two cars are each moving with speeds of 30 m/s, in opposite directions, toward each other. What is the relative velocity of one car with respect to the other? Use the nonrelativistic formula for addition of velocities. Now two rockets are moving with a speed 0.9c (c is the speed of light) towards each other. What is the relative speed of one with respect to other? Use the relativistic formula for addition of velocities. Use the relativistic formula to recalculate the answer in II.1 Speed of light is 3 times 10^8 m/s. You may have to retain many significant figures to see a difference. Two cars are each moving with speeds of 30 m/s, in opposite directions, toward each other. What is the relative velocity of one car with respect to the other? Use the nonrelativistic formula for addition of velocities. Now two rockets are moving with a speed 0.9c (c is the speed of light) towards each other. What is the relative speed of one with respect to other? Use the relativistic formula for addition of velocities. Use the relativistic formula to recalculate the answer in II.1. Speed of light is 3 times 10^8 m/s. You may have to retain many significant figures to see a difference. Compare the results from II.1 and II.3. Explain.

Explanation / Answer

1. two cars of speeds 30 m/s, moving in opposite directions then their relative velocity is

   Let car A moving to the left and car B moving to the right then their relative velocity is

   V = VB-VA
   V = VB-(-VA) = VB+VA

   V = 30+30 = 60 m/s

the relative velocity of cars with each other is 60 m/s

2.
tow rockets moving with 0.9c speed towards each other then the relative velocity is given by
  

   v = U -V / (1-U*V/c^2)

as in 1 v = u+v /(1-uv/c^2)
   = 1.8c/(1-0.9*0.9c^2/c^2)

   = 1.8c /(1-0.81)
   = 9.473684210 c

the relative velocity is V = 9.473684210c

3. 30 m/s = 1*10^-7*c

so    v = u+v /(1-uv/c^2)
   = 2*10^-7c/(1-(1*10^-7*1*10^-7)c^2/c^2)

   = 2*10^-7c
   = 60 m/s

4.no change in the relative velocity of 1 and 3 because these cars are moving with small speeds so no much change

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