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BITSAT2016PhysicsMotion in Two DimensionsActual

A stone projected with a velocity a at an angle with the horizontal reaches maximum height H ₁ . When it is projected with velocity u at an angle ( 2 - ) with the horizontal, it reaches maximum height H ₂ . The relation between the horizontal range R of the projectile, heights H ₁ and H ₂ is

Options

  1. AR =4 H ₁ H ₂
  2. BR =4 ( H ₁- H ₂ )
  3. CR =4 ( H ₁+ H ₂ )
  4. DR = H ₁² H ₂²

Correct answer

A. R =4 H ₁ H ₂

Step-by-step solution

aligned & H ₁= u ² ² 2 ~g and H ₂= u ² ² (90^ - ) 2 ~g = u ² ² 2 ~g H ₁ H ₂=& u² ² 2 ~g u² ² 2 ~g = (u² 2 )² 16 g² = R² 16 R=4 H₁ H₂ aligned

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