# Let's Play Catch!

Classical Mechanics Level pending

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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