L$10-2[10$ marks$]$ A person standing still on a train holds a rod of length $\backslash ($ l $\backslash )($length at rest$).$ The rod leans at an angle $\backslash (\backslash$theta $\backslash )$ with respect to the horizontal direction. The train is moving with speed $\backslash ($ v $\backslash )$ relative to the ground. According to an observer on the ground,

$($a$)$ what is the projected length of the rod along horizontal direction?

$($b$)$ what is the projected length of the rod along vertical direction?

$($c$)$ what is angle between the rod and the horizontal direction?