gud 1 frrom AITS .......[yesterday :P]

lets resolve the impusle delivered into 2 directions...horizontax (X) and vertical (Y)...we know that J_x=Psin\phi
as for P_y we have Pcos\phi - P_y = P'.....1)
and also for angular impulse about the hinge, we have
Pcos\phi * 3L/4
=I w.....2) {where I is the moment of inertia about hinge pt}
and finally we have P'/m = wL/4......3) {constraint eqn.}
jus gievn the brief input...
cheers!!!

completely solving..
Conserving ang momentum,
P₀cosθ*3l/4 = (ml²/12 + ml²/16)ω
==> ω = 3P₀/ml ... putting cosθ = 7/12

Now, P₀sinθ = J_x = 9P₀/12

V_com = l/4*ω = 3P₀/4m
==> P₀cosθ + J_y = m*3P₀/4m
==> 7P₀/12 + J_y = 3P₀/4
==> J_y = 2P₀/12

So hinge impulse = √J_x² + J_y²
= P₀/12*√85