Two small stones \(A ,B\) of masses \(1~kg\) and \(2~kg\) respectively, are projected simultaneously at \(t=0\). The stone \(A\) is projected horizontally with speed \(V_a~ms^{-1}\) from the top of a tower that is \(Y\) meters high and the stone \(B\) is projected from the ground at a distance \(X\) meters from the foot of the tower with speed \(V_b~=~90~ms^{-1}\) at an angle of \(37^o\) with the horizontal as shown in the figure. At time \(t~=~6~sec\) after projection, they collide in air and at that moment their velocities are mutually perpendicular. Then find \(X~+~Y~+~V_a\)

Note: give the sum of the numerical values of \(X, Y , V_a\).

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