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A cannon fires a shell with a speed of 84m/s. When the cannon is inclined at 45`, the horizontal distance covered is observed as 630m. What is the

percentage decrease in the horizontal distance observed due to air resistance?


Using \dfrac {u^{2}sin2\theta }{g} to find the range of the Canon fire shell, we get \dfrac {84^{2}}{10} that is 705.6 But the actual range we got its 640. Hence, calculate the percentage.
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The range of a projectile in two dimensions in the absence of any air resistance:

  horizontal speed = u Cos Ф
  time of flight = 2 * u sin Ф  / g
  So    R = u²/g * Sin 2Ф
             = 84² / 9.81  * Sin (2 * 45° )
            = 719.266 meters.
actual range observed = 630 m

% decrease = 89.266 / 719.266 * 100 = 12.41%

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