Congratulations to this week's winner
Rich Bernstein
Correct solutions also came from Adam Allen, Alex Uskov, Chris Schladt.
Further correct solutions were submitted by Bill Webb, Paul, Augustin Murillo,
Fransesc Suñol i Esquirol, Paul Botham, Nancy Schwarzkopf, Nick
McGrath, Alejandro Vellano, and, of course, the proposer, Jens Voss.
Simple
right angle trigonometry gives you a =
q1-q2
and y / .915 = (y + 11.885) / (x +
2.5) from which you deduce that y = 10.874775 / (x
+ 1.585). You can now express the angles as
q1 = arctan((x
+ 2.5) / 18.285) and q2
= arctan((x + 1.585) / 11.885).
You therefore want to minimize the expression
a = arctan((x
+ 2.5) / 18.285) - arctan((x + 1.585)
/ 11.885).
Differentiating with respect to x and setting
equal to zero gives you the equation
which then yields the equation
6.4x2 -
1.46155x - 1419.17546 =
0
with (postive) root x »
15.00576520. So the tennis player would need to jump about 15 meters
into the air to maximize the serving angle. Quite a jump! As
a
is (clearly) increasing from zero up to this maximum, the higher the player
jumps, the better off he or she is.
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