Answer
(a) The length of the rod is 1.0 meter long according to the Earth observer.
(b) $L = 0.917~m$
Work Step by Step
(a) When the rod is perpendicular to the direction of motion, there is no length contraction. Therefore, the length of the rod is 1.0 meter long according to the Earth observer.
(b) Let $L_0 = 1.0~m$
We can find the length $L$ according to the Earth observer:
$L = L_0~\sqrt{1-\frac{v^2}{c^2}}$
$L = (1.0~m)~\sqrt{1-\frac{(0.40~c)^2}{c^2}}$
$L = 0.917~m$
