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AP EAMCET2005PhysicsMotion in Two Dimensions

A body projected vertically upwards crosses a point twice in its journey at a height h just after t₁ and t₂ seconds. Maximum height reached by the body is

Options

  1. Ag 4 (t₁+t₂ )^2
  2. Bg ( t₁+t₂ 4 )^2
  3. C2 g ( t₁+t₂ 4 )^2
  4. Dg 4 (t₁ t₂ )

Correct answer

C. 2 g ( t₁+t₂ 4 )^2

Step-by-step solution

Time taken by the body to reach the point A is t₁ (During upward journey). The body crosess this point again (during downward journey) after t₂ , i.e., the body takes the time (t₂-t₁ ) to come again at point A . So, the time taken by the body to reach at point B (at maximum height). t=t₁+ ( t₂-t₁ 2 ) [ Time of ascending = Time of descending] t= t₁+t₂ 2 So, maximum height, H= 1 2 g t^2= 1 2 g ( t₁+t₂ 2 )^2=2 g ( t₁+t₂ 4 )^2

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