Ponder This Challenge - January 2000 - Catching baseball

Ponder This Challenge:

We are playing baseball on an airless planet. A fly ball is hit directly towards an outfielder. The fielder can detect the changing angle that the ball makes with the horizon, but cannot directly judge changes in distance (apparent size of the ball), and there is no apparent lateral motion. How does she decide whether to move forward or backward to catch the ball?

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Solution

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  If she is correctly positioned, the derivative of (tangent theta) with respect to time is constant. Put another way, there are constants c and d such that tan(theta)=c*t+d where t=time. This is because the ball's height (above the fielder) is a quadratic function of time, with value 0 when t=0 (i.e. when it reaches the fielder), and its horizontal distance from the fielder is a linear functino of time, also achieving the value 0 when t=0. Dividing, we see that the slope is of the form c*t+d.

Solvers

• John Harvey (1.04.2000 @ 10:20 PM EST)
• Will Hopkins (1.06.2000 @ 12:02 PM EST)
• Jimmy Hu (1.10.2000 @ 4:10 PM EST)
• Dan Peleg (1.10.2000 @ 8:26 PM EST)
• Bruce Hoff (1.11.2000 @ 5:06 PM EST)
• Jimmie Mayfield (1.11.2000 @ 10:20 PM EST)
• Manikantan Srinivansan (1.15.2000 @ 12:34 PM EST)
• Manish C Tayal (1.15.2000 @ 05:25 PM EST)
• Mark Van Peteghem (1.22.2000 @ 05:31 PM EST)
• Shmuel Spiegel (1.25.2000 @ 03:15 PM EST)
• David MacMahon (1.28.2000 @ 02:29 PM EST)
• Reed Green (1.30.2000 @ 05:32 PM EST)
• Nicusor Timneanu (1.31.2000 @ 11:31 AM EST)
• Ming-wei Wang (1.31.2000 @ 02:01 AM EST)