The Physics of Missing the Soccer Net from close range

A couple games ago, my soccer team had ample opportunities to score against Gates Chili. We managed to sky the ball over the net from the six yard line, in the first five minutes of the game. After thinking about how hard it is to miss the goal from this distance, I thought I would compute the angle, theta, needed to clear the crossbar (8ft off the ground) from the 6-yard line.

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Given:

*average velocity of shot ~45ft/s

(this value varies between male/female, and level of play)

*delta x=18ft

*delta y=8ft *g=-9.81 m/s²=-32.12 ft/s²

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Find time in terms of theta:

delta x= (velocity in x direction)(time)

time=(18/(45cos(theta))) s

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Find Minimum Theta:

delta y=(V-initial in y direction)(time)+(0.5)(g)(time)²

8=18tan(theta) - (2.57/cos²(theta))

Solve for theta and get.....

theta must be greater than 32.9 degrees to miss the goal.

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Conclusion: Given that the ball is kicked around 45 ft/s, 32.9^o< theta <90^o would cause the ball to go over the crossbar!