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Motion In A Plane

Question
CBSEENPH11018537

Two projectiles are projected at angles θ and (90°–θ) with same speed. What is the ratio of their time of flight?

Solution
Time of flight is given by fraction numerator 2 space straight u space sinθ over denominator straight g end fraction
So ratio of time of flight = fraction numerator begin display style bevelled fraction numerator 2 space straight u space sinθ over denominator straight g end fraction end style over denominator begin display style bevelled fraction numerator 2 space straight u space sin space left parenthesis 90 to the power of straight o minus straight theta right parenthesis over denominator straight g end fraction end style end fraction space 
                                    equals space fraction numerator sin space straight theta over denominator cos space straight theta end fraction space

equals space tan space theta space thin space colon space 1