Two stones are projected with the same velocity in magnitude bu-Turito

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Physics-

Two stones are projected with the same velocity in magnitude but making different angles with the horizontal. Their ranges are equal. If the angel of projection of one is $pi divided by 3$ and its maximum height is $y subscript 1 end subscript$ , the maximum height of the other will be

Physics-General

$3 y_{1}$
$2 y_{1}$
$\frac{y_{1}}{2}$
$\frac{y_{1}}{3}$

Answer:The correct answer is: $fraction numerator y subscript 1 end subscript over denominator 3 end fraction$ Given $theta subscript 1 end subscript equals pi divided by 3 equals 30 degree$
Horizontal range is same if $theta subscript 1 end subscript plus theta subscript 2 end subscript equals 90 degree$
$therefore theta subscript 2 end subscript equals 90 degree minus 30 degree equals 60 degree$
$y subscript 1 end subscript equals fraction numerator u to the power of 2 end exponent sin to the power of 2 end exponent invisible function application 30 degree over denominator 2 g end fraction$ and $y subscript 2 end subscript fraction numerator u to the power of 2 end exponent sin to the power of 2 end exponent invisible function application 60 degree over denominator 2 g end fraction$
$therefore fraction numerator y subscript 2 end subscript over denominator y subscript 1 end subscript end fraction equals fraction numerator sin to the power of 2 end exponent invisible function application 30 degree over denominator sin to the power of 2 end exponent invisible function application 60 degree end fraction equals open parentheses fraction numerator 1 divided by 4 over denominator square root of 3 divided by 4 end fraction close parentheses to the power of 2 end exponent blank equals fraction numerator 1 over denominator 2 end fraction blank o r blank y subscript 2 end subscript equals fraction numerator y subscript 1 end subscript over denominator 3 end fraction$

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