There are two angles of projection for which horizontal range is the same. Show that product of their time of flights is directly proportional to the horizontal range? from Physics Motion in A Plane Class 11 Manipur Board
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There are two angles of projection for which horizontal range is the same. Show that product of their time of flights is directly proportional to the horizontal range?

The angles of projection, for which horizontal range is same, are θ and 90° – θ.

Time of flight for angle of projection θ is,

                       space straight T subscript 1 equals fraction numerator 2 usinθ over denominator straight g end fraction

Time of flight corresponding to angle of projection (90°–θ) is, 

                  straight T subscript 2 equals fraction numerator 2 usin left parenthesis 90 degree minus straight theta right parenthesis over denominator straight g end fraction equals fraction numerator 2 straight u space cosθ over denominator straight g end fraction

Now, product of their time flight is, 

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space space equals fraction numerator 2 straight u squared 2 sinθ space cosθ over denominator gg end fraction        

           
equals fraction numerator 2 straight u squared space sin space 2 straight theta over denominator gg end fraction equals fraction numerator 2 straight R over denominator straight g end fraction            

That is,

                        straight T subscript 1 straight T subscript 2 space proportional to space straight R

Hence proved the relation. 
                      
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