A rocketship 100m long on the earth is moving with 0.9c.How much it's length will appear to an observer on the earth?

1 Answer
1s2s2p
May 19, 2018

#44m#

Explanation:

An object moving at a speed #v# relative to an observer will appear to contract from both frames of reference, though with the object's frame of reference it is the observer being contracted. This happens all the time but the speeds are always too slow to have any noticeable effect, only being noticeable at relativistic speeds.

Formula for length contraction is #L=L_0sqrt(1-v^2/c^2)#, where:

  • #L# = new length (#m#)
  • #L_0# = original length (#m#)
  • #v# = speed of object (#ms^-1#)
  • #c# = speed of light (#~3.00*10^8ms^-1#)

So,
#L=100sqrt(1-(0.9c)^2/c^2)#

#=100sqrt(1-0.9^2)#

#=100sqrt(1-0.81)#

#=100sqrt0.19#

#~~100(0.44)#

#=44m#

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