Answer
a) $L=1.8m$
b) $\theta=78.8^{\circ}$
Work Step by Step
(a) We know that
$L=L_{\circ}\sqrt{1-\frac{v^2}{c^2}cos^2\theta_{\circ}}$
We plug in the known values to obtain:
$L=(2.5m)\sqrt{1-\frac{(0.98c)^2}{c^2}cos^2 45^{\circ}}$
This simplifies to:
$L=2.5m(0.72)$
$L=1.8m$
(b) We know that
$tan\theta=\frac{tan\theta_{\circ}}{\sqrt{1-\frac{v^2}{c^2}}}$
We plug in the known values to obtain:
$tan\theta=\frac{tan 45^{\circ}}{\sqrt{1-\frac{(0.98c)^2}{c^2}}}$
This simplifies to:
$\theta=78.8^{\circ}$
