Question

Penguin #1 travels at speed v=0.9 c relative to penguin #2. At the instant that both are at the origin, they synchronize their clocks to both read 1:00 AM. Penguin #1 reports that her meter stick has length one meter. If #2 were to measure the length of the meter stick of #1, what would he observe its length to be?

Answer 1

Answer:

L = 0.44 [m]

Explanation:

Here we can use the Lorentz transformation related to length to solve it:

$L=L_{0}\sqrt{1-\beta^{2}}$

Where:

L₀ is the length of the moving reference frame (penguin #1)

L is the length of the fixed reference frame (penguin #2)

β is the ratio between v and c

We know that v = 0.9c so we can find β.

$\beta = \frac{0.9c}{c}=0.9$

$L=1 [m]\sqrt {1-0.9^{2}} = 0.44 [m]$

Therefore, the length of the meter stick of #1 observed by #2 is 0.44 m.

I hope it helps you!