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A projectile is projected with velocity k v subscript e end subscript in vertically upward direction from the ground into the spaceblank left parenthesis v subscript e end subscript is the escape velocity andk less than 1 right parenthesis. If air resistance is considered to be negligible then the maximum height from the center of earth to which it can go will be left parenthesis R equals r a d u s blank o f blank e a r t h right parenthesis

  1. fraction numerator R over denominator k to the power of 2 end exponent plus 1 end fraction  
  2. fraction numerator R over denominator k to the power of 2 end exponent minus 1 end fraction  
  3. fraction numerator R over denominator 1 minus k to the power of 2 end exponent end fraction  
  4. fraction numerator R over denominator k plus 1 end fraction  

The correct answer is: fraction numerator R over denominator 1 minus k to the power of 2 end exponent end fraction


    K i n e t i c blank e n e r g y equals p o t e n t i a l blank e n e r g y
    fraction numerator 1 over denominator 2 end fraction m open parentheses k v subscript e end subscript close parentheses to the power of 2 end exponent equals fraction numerator m g h over denominator 1 plus fraction numerator h over denominator R end fraction end fraction
    ⟹ fraction numerator 1 over denominator 2 end fraction m k to the power of 2 end exponent 2 g R equals fraction numerator m g h over denominator 1 plus fraction numerator h over denominator R end fraction end fraction ⟹ h equals fraction numerator R k to the power of 2 end exponent over denominator 1 minus k to the power of 2 end exponent end fraction
    H e i g h t blank o f blank p r o j e c t i l e blank f r o m blank t h e blank e a r t h ’ s blank s u r f a c e equals h
    H e i g h t blank f r o m blank c e n t r e blank r equals R plus h equals R plus fraction numerator R k to the power of 2 end exponent over denominator 1 minus k to the power of 2 end exponent end fraction
    B y blank s o l v i n g blank r equals fraction numerator R over denominator 1 minus k to the power of 2 end exponent end fraction

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