Optimal shot on goal

Calculus Level 2

In a soccer match, the striker \((\)point \(S)\) has beaten all defenders and is running parallel to the sideline towards the goal line. At what distance \(x\) from the goal line should the striker shoot at the goal for the best chance of a goal? Give the result in meters and round to one decimal place.

\(\)
Details and Assumptions:

  • The striker will shoot the ball in a straight line on the ground.
  • The striker isn't perfectly accurate, so his shot may be slightly off from where he intends.
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