Spaceship $"$B$"$ takes over Spaceship $"$A$"$ on an intergalactic highway at a speed of $0\mathrm{.}6$ times the speed of light. Observers in $"$A$"$ equipped with high$-$tech measuring devices find the length of spaceship $"$B$"$ to be $180$ m $.$

a$)$ What is the proper length of $"$B$"?$

b$)$ How long does it take for the entire spaceship $"$B$"$ to pass in front of the observer in $"$A$,"$ who is looking at $"$B$"$ through a small window

$1.$ According to the observer in $"$A$"!$

$2.$ According to observers in $"$B$"?$

Use $\backslash ($ c$=2\mathrm{.}99\backslash$times $10^\{8\}\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$