Physics-
General
Easy

Question

Two stones are projected from the same speed but making different angels with the horizontal. Their horizontal ranges are equal. The angle of projection of one is pi divided by 3 and the maximum height reached by it is 102 m. Then maximum height reached by the other in metre is

  1. 336  
  2. 224  
  3. 56  
  4. 34  

The correct answer is: 34


    We know that if two stones have same horizontal range, then this implies that both are projected at theta and 90 degree minus theta.
    G i v e n comma blank theta equals fraction numerator pi over denominator 3 end fraction equals 60 degree
    therefore blank 90 degree minus theta equals 90 degree minus 60 degree equals 30 degree
    For first stone,
    M a x i m u m blank h e i g h t equals 102 equals fraction numerator u to the power of 2 end exponent s i n to the power of 2 end exponent 60 degree over denominator 2 g end fraction
    For second stone,
    M a x i m u m blank h e i g h t comma blank h equals fraction numerator u to the power of 2 end exponent s i n to the power of 2 end exponent 30 degree over denominator 2 g end fraction
    therefore blank fraction numerator h over denominator 102 end fraction equals fraction numerator s i n to the power of 2 end exponent 30 degree over denominator s i n to the power of 2 end exponent 60 degree end fraction equals fraction numerator open parentheses 1 divided by 2 close parentheses to the power of 2 end exponent over denominator open parentheses square root of 3 divided by 2 close parentheses to the power of 2 end exponent end fraction
    o r blank h equals 102 cross times fraction numerator 1 divided by 4 over denominator 3 divided by 4 end fraction equals 34 blank m

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