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Introductory Physics Homework Help
What is the best shape for a soccer goal post?
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[QUOTE="haruspex, post: 6530610, member: 334404"] If the ball comes from ##(D,\theta)## in polar then, of the whole ##2\pi## range of angles it can go in, only a sector of angle width ##\theta## is headed for the goal. The probability of a goal is therefore ##\frac \theta{2\pi}##. Integrating, the overall probability is ##\frac 1\pi\int_0^\pi\frac \theta{2\pi}.d\theta=\frac 14##. The probability we calculated before is what I defined it to be: the probability of a goal if the angle of the trajectory is uniformly distributed over its legal range ##(\pi)## and its displacement from the centre of the post is uniformly distributed over (-D,D). Changing it to the shot being made from an arc of radius D, uniformly distributed along the arc, leads to a different distribution of trajectories and a different probability. I note that throughout this thread you have not really understood the importance of clearly defining the assumed distribution. This is fundamental to dealing with probabilities. [/QUOTE]
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What is the best shape for a soccer goal post?
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