Length Contraction Relativity Question

[goldilocks]

Hello, I am not sure if I am doing this right or not. It seems to simple to be the right aswer, I feel I must have gone wrong somewhere. Many thanks :-) xxx

Homework Statement

Length Contraction Relativity Question?

An aeroplane is of length L’(m) precisely when measured in its rest frame at the airport. In what percentage it will contract if measured by the same ground-based observer if it was flying past at 900 km.p.h?
[Here you may need Taylor’s expansion]

Homework Equations

Lmoving= Lrest x SQR[1 - (V/C)^2]

The Attempt at a Solution

I have tried to start this. I used Lmoving= Lrest x SQR[1 - (V/C)^2]

Lrest = L'(m)

Lmoving = L'(m)
= L'(m) x SQR(1-(250^2/(3x10^8)^2)
= L'(m) x SQR (1- 6.9445x10^-13)
= L'(m) x SQR (1)
= L'(m)

So there is no contraction as v is not near enough to c for realtivity to take effect. Is this right? I didn't use taylor expansion, so have I gone wrong somewhere. Thanks a lot. xxx

 

[Doc Al]

So there is no contraction as v is not near enough to c for realtivity to take effect. Is this right?

No. Since the speed is small compared to c, the effect will be small. But you can still calculate it.

I didn't use taylor expansion, so have I gone wrong somewhere.

Hint: Look up the Taylor expansion of \sqrt{1 + x}, where x << 1.