Let's Play Catch!

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.