Passing the ball

Worked example 1: how high must a lob go? A passer releases the ball 2.2 m above the floor to a receiver 6 m away who catches it at the same height. A defender 1 m away can jump and reach 2.7 m. For a projectile that lands at the same height after a distance $RR$, the height above the release point at a distance $xx$ is

1. At the defender, $x=1x\; =\; 1$, $R=6R\; =\; 6$: the ball must rise at least $2.7-2.2=0.5\mathrm{m}2.7\; -\; 2.2\; =\; 0.5\backslash ,\backslash mathrm\{m\}$, so $\tan \theta \times \frac{5}{6}\ge 0.5\backslash tan\backslash theta\; \backslash times\; \backslash frac\{5\}\{6\}\; \backslash ge\; 0.5$, $\tan \theta \ge 0.6\backslash tan\backslash theta\; \backslash ge\; 0.6$ and $\theta \ge {31}^{\circ }\backslash theta\; \backslash ge\; 31^\{\backslash circ\}$.
2. At 35°: height over the defender $2.2+0.700\times \frac{5}{6}=2.78\mathrm{m}2.2\; +\; 0.700\; \backslash times\; \backslash frac\{5\}\{6\}\; =\; 2.78\backslash ,\backslash mathrm\{m\}$; peak $2.2+\frac{R\tan \theta }{4}=2.2+1.05=3.25\mathrm{m}2.2\; +\; \backslash frac\{R\backslash tan\backslash theta\}\{4\}\; =\; 2.2\; +\; 1.05\; =\; 3.25\backslash ,\backslash mathrm\{m\}$.
3. Speed and time: $v=\sqrt{\frac{gR}{\sin 2\theta }}=\sqrt{\frac{9.81\times 6}{\sin {70}^{\circ }}}=7.9\mathrm{m}{\mathrm{s}}^{-1}v\; =\; \backslash sqrt\{\backslash frac\{gR\}\{\backslash sin\; 2\backslash theta\}\}\; =\; \backslash sqrt\{\backslash frac\{9.81\; \backslash times\; 6\}\{\backslash sin\; 70^\{\backslash circ\}\}\}\; =\; 7.9\backslash ,\backslash mathrm\{m\backslash ,s^\{-1\}\}$; time in the air $\frac{2v\sin \theta }{g}=0.93\mathrm{s}\backslash frac\{2v\backslash sin\backslash theta\}\{g\}\; =\; 0.93\backslash ,\backslash mathrm\{s\}$.

A flat chest pass over the same 6 m at $10\mathrm{m}{\mathrm{s}}^{-1}10\backslash ,\backslash mathrm\{m\backslash ,s^\{-1\}\}$ takes 0.6 s. The lob clears the defender but gives the defence half as long again to move, so it is used only when the flat pass is blocked and the receiver has space. The reach and release heights are illustrative.

1. From the centre pass, the Centre throws the ball over the whole centre third, and the Goal Attack catches it standing in the goal third. Illegal: over a third. Free pass to the other team, taken by the transverse line where the ball entered the goal third.
2. The Wing Attack, 0.5 m from the Goal Shooter, hands the ball to her with no space for any defender to reach it. Illegal: a short pass.
3. The Goal Defence bounces the ball once to the Wing Defence 5 m away. Legal.
4. A player passes, the ball hits nobody, and she runs on and catches it again. Illegal: she may not play the ball again until it has touched another player or the goalpost.