$(2$ pt$)$ A particle of mass $m$ is projected from point A with an initial velocity $v_0$ perpendicular to line $OA$ and moves under a central force $F$ along a semicircular path of diameter $OA.$

$($a$)$ Observing that $r=r_{0}cos$ and using the equation $r^2{}^{}=h($where $h$ is the angular momentum per unit mass$),$ show that the speed of the particle is $v=\frac{v_0}{co{s}^2}.($Hint: what is $h$ at point $A?)$

$($b$)$ Determine the tangential component $F_t$ of the central force $F$ along the tangent to the path of the particle for $=45.$