Answer
$L'=49m$
Work Step by Step
Find the value of gamma using the formula $$\gamma=\frac{1}{\sqrt{1-\beta^2}}$$ Substituting the known value of $\beta=0.65$ ($v=\beta c$) gives $$\gamma=\frac{1}{\sqrt{1-0.65^2}}=1.32$$ The formula for length contraction is $$L'=\frac{L}{\gamma}$$ Substituting the known values of $L=64m$ and $\gamma=1.32$ yields a contracted length of $$L'=\frac{64m}{1.32}=49m$$
