P and Q are playing catch. In our coordinate system P is standing at \((0,0,0)\) and Q is standing at \((80m,0,0)\). The playground is the XY plane.

P throws the ball with a velocity \(5\hat i +12\hat j+49 \hat k\) in \(m/s\). Let \(a\hat i+b\hat j\) be the velocity of Q so that he can catch the ball before it falls to the ground. Find \(|ab|\) to the nearest integer.

**Details and Assumptions:**

- Take \(\vec g= -9.8 \hat k\) in \(m/s^2\)
- Assume both P and Q throw and catch the ball from the same height.

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