A knight on horseback holds a 9.0-m lance.The horse can run at 0.75c.(It wins most of its races!)How long will the lance appear to a person that is standing still on the ground as the horse runs past?
A)6.0 m
B)14 m
C)9 m
D)6.8 m
E)4.5 m

Question

A knight on horseback holds a 9.0-m lance.The horse can run at 0.75c.(It wins most of its races!)How long will the lance appear to a person that is standing still on the ground as the horse runs past?
A)6.0 m
B)14 m
C)9 m
D)6.8 m
E)​4.5 m

Quizplus · Accepted Answer

The length contraction formula in special relativity is $L = L_0\sqrt{1-v^2/c^2}$, where $L_0$ is the rest length (9.0 m in this case), $v$ is the velocity of the moving object (0.75c), and $c$ is the speed of light. Plugging in the values, we get $L = 9.0\sqrt{1-0.75^2} = 9.0\sqrt{1-0.5625} = 9.0\sqrt{0.4375} \approx 6.0$ m.

A Knight on Horseback Holds a 9