Question

A 3.0-meter stick moves at a speed of 0.90c relative to an observer. The stick is aligned parallel to the direction ofmotion. What is the observed length of the stick?(a) 6.9 m(b) 4.2 m(C) 2.7 m(d) 1.3 m

Answer 1

In order to determine the observed length of the stick, use the following formula for the length contraction due to the relativistic speed of the stick (this formula can be used because the motion of the stick is in the same direction of the axis of the stick):

`L=L_0\sqrt[]{1-(v^2)/(c^2)}`

where:

L: observed length of the stick = ?

Lo: length of the stick in its reference system = 3.0 m

v: speed of the stick = 0.90c

replace the previous values of the paramters into the formula for L:

`\begin{gathered} L=(3.0m)\sqrt[]{1-((0.9c)^2)/(c^2)} \\ L=(3.0m)\sqrt[]{1-0.81} \\ L=(3.0m)(0.43)=1.3m \end{gathered}`

Hence, the observed length of the stick is 1.3m