A gun is fired with muzzle velocity 1114 feet per second at a target 4950 feet away. Find the minimum angle of elevation necessary to hit the target. Assume the initial height of the bullet is 0 feet, neglect air resistance, and give your answer in degrees.

Answer :

Answer:

The elevation angle is  [tex]\theta = 3.67^o[/tex]

Explanation:

From the question we are told that

   The velocity is  [tex]u = 1114\ ft/s[/tex]

    The range of the bullet projection is   [tex]R = 4950 \ ft[/tex]

     The initial height of bullet is  [tex]h_1 = 0 \ ft[/tex]

Range of this bullet projection is mathematically represented as

          [tex]R = \frac{u^2 sin (2 \theta )}{g}[/tex]

=>      [tex]\theta = \frac{sin ^{-1} [\frac{R * g }{ u^2} ]}{2}[/tex]

Here  [tex]g = 32 ft/s^2[/tex]

substituting values

         [tex]\theta = \frac{sin ^{-1} [\frac{4950 * 32 }{ 1114^2} ]}{2}[/tex]

        [tex]\theta = 3.67^o[/tex]

 

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