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AP EAMCET202017 Sep 2020Evening ShiftPhysicsMotion in One DimensionActual

A ball is projected upwards from a height (h ) above the surface of the earth with velocity (v ). The time at which the ball strikes the ground is

Options

  1. A( v g [1+ 2 g h v^2 ] )
  2. B( v g [1- 1+ 2 h g ] )
  3. C( v g [1+ 1+ 2 g h v^2 ] )
  4. D( v g [1+ v^2+ 2 g v^2 ] )

Correct answer

C. ( v g [1+ 1+ 2 g h v^2 ] )

Step-by-step solution

The given situation is shown in the following figure. If time taken by the ball to reach at highest point (A ) is (t ), then (0=v-g t t= v g ) Total time taken to reach the ball from point of projection to reach at point (B ) is given as (t₁=t+t=2 t t₁= 2 v g ) If (t₂ ) be the time taken by the ball to reach from point (B ) to point (C ), then ( aligned h & =v t₂+ 1 2 g t₂^2 g t₂^2+2 v t₂-2 h=0 t₂ & = -2 v 4 v^2+8 g h 2 g t₂ & = -v g + v^2+2 g h 2 aligned ) [taking +ve sign because time is positive] ( ) Total time,

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