A particle $P$ is projected with speed $26{\text{ }}m{\text{ }}{s^{ - 1}}$ at an angle of ${30^ \circ }$ above the horizontal from a point $O$ on a horizontal plane.
a) For the instant when the vertical component of the velocity of $P$ is $5{\text{ }}m{\text{ }}{s^{ - 1}}$ downwards, find the direction of motion of $P$ and the height of $P$ above the plane.
b) $P$ strikes the plane at the point $A$. Calculate the time taken by $P$ to travel from $O$ to $A$ and the distance $OA$.
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