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Question

A ball is thrown from the ground to clear a wall 3 m high at a distance of 6 m and falls 18 m away from the wall. Find the angle of projection of ball.


A
tan1(13)
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B
tan1(23)
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C
tan1(32)
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D
tan1(35)
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Solution

The correct option is C $$\displaystyle \tan ^{-1}\left ( \frac{2}{3} \right )$$
$$R=6+18=24m=\frac { { u }^{ 2 }sin2\theta  }{ g } \Rightarrow { u }^{ 2 }=\frac { 240 }{ 2sin\theta cos\theta  } =\frac { 120 }{ sin\theta cos\theta  } \\ y=xtan\theta -\frac { g{ x }^{ 2 } }{ 2{ u }^{ 2 }{ cos }^{ 2 }\theta  } \Rightarrow 3=6tan\theta -\frac { 360 }{ 2{ u }^{ 2 }{ cos }^{ 2 }\theta  } \\ \Rightarrow 3=6tan\theta -\frac { 360 }{ 240 } tan\theta =\frac { 9 }{ 2 } tan\theta \Rightarrow tan\theta =\frac { 2 }{ 3 } $$

Physics

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