Messi's goal

In the final match of the UEFA champions league, Messi has to hit the goal from \(2\text{ m}\) away from it. The height of the goal is \(3\text{ m}\). There is one fantastic knowledge with Messi that the goalkeeper can stop the ball only at max \(2.5\text{ m}\) high.

Also, Messi hits the ball with initial speed \(\sqrt{3}\text{ m/s}\). Find the range of tan(angle) at which there is 100% possibility Messi will hit the goal.

Details and Assumptions:

  1. No player is stopping him i.e. no player is in between Messi and goalkeeper.
  2. Consider only gravity. Forget about magnus effect ,air resistance, etc.
  3. Take \(g=10 \text{ m/s}^2 \).

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