Homework question on special relativity

[spaghetti3451]

Homework Statement

Samantha, Tom, and Roberta are triplets.

(i) Samantha is an airline pilot who flies along a straight flight path at 300 ms^-1 for 80 hours per month (in her rest frame). How much younger will she be than her brother Tom (who handles baggage at the airport) when she retires after 30 years?

Homework Equations

Time dilation formula

The Attempt at a Solution

Use the time dilation formula t = γt₀, where t is the time in the moving frame (that of Tom) and t₀ is the time in the rest frame (that of Samantha).

t₀ = (3600*80*12*30) = 103680000 s
v = 300 ms^-1

Therefore, t = t₀ + (51.84 ms), using the binomial expansion in the calculation.

So, Samantha will be 51.84 ms younger when she retires after thirty years.

Could you please confirm if I am right?

 

[Doc Al]

Seems like you're off by a few powers of 10. (Unless I messed up the calculation.)

What did you get for γ-1?

 

[spaghetti3451]

I think I have spotted the error. Is your answer in microseconds rather than milliseconds?

 

[spaghetti3451]

i.e. 51.84 microseconds.

 

[Doc Al]

That's it. μs, not ms.