Two projectiles are projected with same speed but at different angles. Under what conditions can they land at the same point at the same time on the earth? from Physics Motion in A Plane Class 11 Manipur Board
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Two projectiles are projected with same speed but at different angles. Under what conditions can they land at the same point at the same time on the earth?

Given, two projectiles are projected at different angles with the same speed. 

So, the two angles of projection i.e. θ and 90°–θ, for which horizontal range is same.

The projectiles will land at the same point if they are projected at angles θ and (90°–θ) from the same point and in the same plane. But, since the time of flight is different for the two cases, therefore the projectiles will reach the ground at different moments. 

If the projectile that takes more time to reach the ground is projected earlier than the second, then both may reach the ground at the same moment. 

Time of flight of first projectile projected at angle θ, straight T subscript 1 equals fraction numerator 2 straight u space sin space straight theta over denominator straight g end fraction

Time of flight of second projectile projected at angle 90°–θ,
straight T subscript 2 equals fraction numerator 2 straight u space cosθ over denominator straight g end fraction 

If two projectiles are projected at the time interval, then they will land at the same time. 

             straight T subscript 1 minus straight T subscript 2 equals fraction numerator 2 straight u over denominator straight g end fraction left parenthesis sin space straight theta space minus space cos space straight theta right parenthesis

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