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Physics-

General

Easy

Question

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

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

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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