A spear is thrown at a very high speed. As it passes, you measure its length to be half its normal length. From this you conclude that the spear must be moving at
A) 1.00 c
B) 0.866 c
C) 0.707 c
D) 0.500 c
E) Not enough information

Question

Quizplus · Accepted Answer

According to the theory of relativity, the length contraction formula is $L = L_0\sqrt{1 - \frac{v^2}{c^2}}$, where $L$ is the observed length, $L_0$ is the rest length, $v$ is the velocity of the object, and $c$ is the speed of light. If the observed length $L$ is half of the rest length $L_0$, then we have $0.5 = \sqrt{1 - \frac{v^2}{c^2}}$. Squaring both sides gives $0.25 = 1 - \frac{v^2}{c^2}$, which simplifies to $\frac{v^2}{c^2} = 0.75$. Taking the square root of both sides gives $\frac{v}{c} = \sqrt{0.75} = 0.866$, meaning the spear must be moving at 0.866 times the speed of light.

A Spear Is Thrown at a Very High Speed