Answer
(a) $0.75 m \times 0.75m \times 0.36m$ (b) $V'=0.20 m^3$
Work Step by Step
(a) Find the value of gamma using the equation $$\gamma=\frac{1}{\sqrt{1-\beta^2}}$$ Substituting the known value of $\beta=0.88$ $(v=\beta c)$. $$\gamma=\frac{1}{\sqrt{1-0.88^2}}=2.1$$ Use the length contraction formula $$L'=\frac{L}{\gamma}$$ and known values of $L=0.75m$ and $\gamma=2.1$ to get a contracted length of $$L'=\frac{0.75m}{2.1}=0.36m$$ Only the dimension of motion is contracted, so all other dimensions are 0.75m. The dimensions are now $0.75 m \times 0.75m \times 0.36m$. (b) The volume of a rectangular prism is equal to $$V=lwh$$ Substituting the known values of $l=0.75m$, $w=0.36m$, and $h=0.75m$ yields a volume of $$V'=(0.75m)(0.75m)(0.36m)=0.20m^3$$
