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Motion in A Plane

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
Show that there are two angles of projection for which horizontal range is the same.

Horizontal range is given by,

                   straight R equals fraction numerator straight u squared sin 2 straight theta over denominator straight g end fraction
where, straight theta is the angle of projection and is less than 90 degree.

We know, sin left parenthesis 180 degree minus 2 straight theta right parenthesis space equals space sin space 2 straight theta
rightwards double arrow             sin space 2 left parenthesis 90 degree minus straight theta right parenthesis space equals space sin space 2 straight theta

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#6 {main}</pre>         [Where straight alpha equals 90 degree minus straight theta]

Now,  

         straight R subscript 0 equals fraction numerator straight u squared sin 2 straight theta over denominator straight g end fraction  and  straight R subscript straight alpha space equals space fraction numerator straight u squared space sin 2 straight alpha over denominator straight g end fraction

Since     sin space 2 straight theta space equals space sin space 2 straight alpha

∴            straight R subscript 0 equals straight R subscript straight alpha

Thus horizontal range is the same for angle of projection θ and α = 90°–θ. 

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