Two particles are projected from the same point with the same speed u such that they have the same rang R, but different maximum heights h_{1} and h_{2}. Which of the following is correct?

  • Option 1)

    R^{2}=4h_{1}h_{2}

     

  • Option 2)

    R^{2}=16h_{1}h_{2}

  • Option 3)

    R^{2}=2h_{1}h_{2}

  • Option 4)

    R^{2}=h_{1}h_{2}

 

Answers (1)

R is the same for \theta and (90-\Theta ) angle of projection 

R=\frac{2u^{2}\sin \Theta \cos \Theta }{g},     h_{1}=\frac{u^{2}\sin ^{2}\Theta }{2g},     h_{2}=\frac{u^{2}\cos ^{2}\Theta }{2g}

R^{2}=\frac{4u^{2}\sin ^{2}\Theta }{g}  \frac{u^{2}\cos ^{2}\Theta }{g}

R^{2}=4.2h_{1}\cdot 2h_{2}=16h_{1}h_{2}


Option 1)

R^{2}=4h_{1}h_{2}

 

Option 2)

R^{2}=16h_{1}h_{2}

Option 3)

R^{2}=2h_{1}h_{2}

Option 4)

R^{2}=h_{1}h_{2}

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