Rocket Velocity: γ = 4, v = √15/4c

[billy92]

If a rocket is traveling past the Earth at speed v, and the time interval measured by the astronaut is four times smaller than the time interval measured by an observer on the Earth. What is the value of v

I have attempted the solution and got:

Δt=γΔt'

Where i believe that gamma will be 4.

From this i used:

γ=$\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$

From this i managed to calculate v=$\frac{\sqrt{15}}{4}$c

However i am slightly concerned about how large this value is for a rocket but cannot seem to see any other solution to this problem. Any suggestions?

Thanks

 

[ghwellsjr]

Yes, you are right, it takes very large values of velocity to get appreciably large values of gamma. You got the right answer.

 

[billy92]

Yes, you are right, it takes very large values of velocity to get appreciably large values of gamma. You got the right answer.

Thanks for the quick reply.