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## Homework Statement

If a clock in an airplane is found to slow down by 5 parts in 10

^{13}, (i.e. Δt/Δt

_{o}= 1 + 5x10

^{-13}), at what speed is the airplane travelling? (Hint: You may need to use the binomial expansion for γ.)

To be honest, I'm really confused about what this question's telling me. What's in the brackets?

## Homework Equations

γ = 1/√(1-v

^{2}/c

^{2})

That's the equation I used.

## The Attempt at a Solution

When I rearranged the equation to find the velocity, I got v = √((1-(1/γ)

^{2})(c

^{2}))

I subbed in 1 + 1.5x10

^{-13}for γ but I keep getting 0 as my velocity and the answer's supposed to be 300 m/s. Am I even doing this right? Thanks in advance! I appreciate any help you can give me!