Object \(A\) is thrown horizontally from a height of \(\overline{OA}=h\) at a speed of \( v_A.\) At the same time, object \(B\) which is \(\overline{OB}=\frac{h}{2}\) away from \(O\) on the ground is thrown upward perpendicularly to the ground at a speed of \(v_B.\) What is the ratio \(\displaystyle{ \frac{v_A}{v_B} }\) when the two objects \( A \) and \( B \) collide?

Gravitational acceleration is \(g= 10\) m/s\(^2 \).

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