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KCET2016PhysicsMotion in Two Dimensions

Three projectiles ( A, B ) and ( C ) are projected at an angle of ( 30^ , 45^ , 60^ ) respectively. If ( R_ A , R_ B ) and ( R_ C ) are ranges of ( A, B ) and ( C ) respectively, then (velocity of projection is same for ( A ), ( B & C) )

Options

  1. A( R_ A =R_ B =R_ C )
  2. B( R_ A =R_ C >R_ B )
  3. C( R_ A < R_ B < R_ C )
  4. D( R_ A =R_ C < R_ B )

Correct answer

D. ( R_ A =R_ C < R_ B )

Step-by-step solution

Given, angle of projection of A=30^ ; angle of projection of B=45^ ; angle of projection of C=60^ . Range of A=R A ; rangeof B=R_ B irange of C=R_ C Now, Horizontal range = ( Initial velocity )² (2 Launch angle ) 2 Acceleration due to gravity R= v₀² 2 g R 2 R_ A (2 30^ )= (60^ ) R_ A = 3 2 R_ B (2 45^ )= (90^ ) R_ B =1R_ C (2 60^ )= (120^ ) R_ C = 3 2 Thus, R_ A =R_ C < R_ B

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