A classical mechanics problem by Guilherme Dela Corte

A fixed cannon fires a projectile with initial speed of \( 20\text{ m/s} \) and an angle of \( \frac{\pi}{3} \) rad with respect to the horizontal ground.

In the highest point of its trajectory, the projectile explodes into two fragments of equal mass. One of these has no instantaneous velocity in the moment after the explosion, and falls vertically.

At what distance from the cannon does the second fragment fall?

Give your answer to the nearest integer.

Details and Assumptions:

  • Ignore any dissipative effects of the air on the projectile and its fragments.
  • Consider \( g = 9.81 \text{ m/s}^2\).
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