From the top of a tower of height h a body of mass m is projected in the horizontal direction with a velocity v , it falls on the ground at a distance x from the tower. If a body of mass 2 m is projec

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From the top of a tower of height h a body of mass m is projected in the horizontal direction with a velocity v , it falls on the ground at a distance x from the tower. If a body of mass 2 m is projected from the top of another tower of height 2 h in the horizontal direction so that it falls on the ground at a distance 2x from the tower, the horizontal velocity of the second body is -

TestHub · Accepted Answer

Let t be the time of flight. For horizontal projection, h = 2 1 ​ g t 2 , so t = g 2 h ​ ​ . The horizontal distance is x = v t . For the first case: x = v g 2 h ​ ​ . For the second case: 2 x = v ′ g 2 ( 2 h ) ​ ​ = v ′ 2 ​ g 2 h ​ ​ . Dividing the two equations: x 2 x ​ = v g 2 h ​ ​ v ′ 2 ​ g 2 h ​ ​ ​ . 2 = v v ′ 2 ​ ​ , so v ′ = 2 2 ​ v ​ = 2 ​ v .

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