Suppose you take an 80 million km trip to Mars from Earth traveling at 0.8c. Unb

Question

Suppose you take an 80 million km trip to Mars from Earth traveling at 0.8c. Unbeknownst to you, your mortal enemy has placed a bomb on your spaceship with a 4 minute timer.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

Will you live long enough to reach Mars before the bomb explodes?

Answer this problem first without using relativity.

Then answer it from the point of view of your Earth-bound enemy.

And lastly, answer it from your point of view inside the spaceship.

Explanation / Answer

Part A)

4 minutes is 240 sec, so you have to be there in less than 240 sec

In non-relativistic terms

d = vt

80000 X 10^6 = (.8)(3 X 10^8)(t)

t = 333 sec (so you would explode)

Part B)

From the earth bound enemy, time dilates

t = t'/(1 - v^2/c^2)^.5

t = 240/(1 - .8^2)^.5

t = 400 seconds before the explosion happens, so he would think you got there safely

Part C)

In your terms, the length of travel is smaller

L = (8 X 10^10)(1 - v^2/c^2)^.5

L = 4.8 X 10^10 m

4.8 X 10^10 = (.8)(3 X 10^8)(t)

t = 200 sec

So you would get to your destination in only 200 seconds, you would have another 40 seconds before the explosion, so you would be safe.

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