Physics-
General
Easy

Question

For an object thrown at 45 degree to horizontal, the maximum height left parenthesis H right parenthesis and horizontal range (R ) are related as

  1. R equals 16 H  
  2. R equals 8 H  
  3. R equals 4 H  
  4. R equals 2 H  

The correct answer is: R equals 4 H


    The range of particle is
    R equals fraction numerator u to the power of 2 end exponent s i n 2 theta over denominator g end fraction
    R equals fraction numerator u to the power of 2 end exponent s i n 2 cross times 45 degree over denominator g end fraction open parentheses therefore theta equals 45 degree close parentheses
    o r blank R equals fraction numerator u to the power of 2 end exponent s i n 90 degree over denominator g end fraction
    o r blank R equals fraction numerator u to the power of 2 end exponent over denominator g end fraction blank open parentheses i close parentheses

    Now, the maximum height of the particle is
    H equals fraction numerator u to the power of 2 end exponent s i n to the power of 2 end exponent theta over denominator 2 g end fraction
    equals fraction numerator u to the power of 2 end exponent s i n to the power of 2 end exponent 45 degree over denominator 2 g end fraction equals fraction numerator u to the power of 2 end exponent open parentheses fraction numerator 1 over denominator square root of 2 end fraction close parentheses to the power of 2 end exponent over denominator 2 g end fraction
    equals fraction numerator u to the power of 2 end exponent over denominator 4 g end fraction blank open parentheses i i close parentheses
    Dividing Eqs. (i) by Eq. (ii),
    fraction numerator R over denominator H end fraction equals fraction numerator u to the power of 2 end exponent divided by g over denominator u to the power of 2 end exponent divided by 4 g end fraction
    o r blank R equals 4 H

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