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Physics-

General

Easy

Question

Two particles 1 and 2 are projected with same speed $v$ as shown in figure. Particle 2 is on the ground and particle 1 is at a height $h$ from the ground and at a horizontal distance $s$ from particle 2. If a graph is plotted between $v$ and $s$ for the condition of collision of the two then ( $v$ on $y$ -axis and $s$ on $x$ -axis

It will be a parabola passing through the origin
It will be straight line passing through the origin and having a slope of $\sqrt{\frac{g}{8 h}}$
It will be a straight line passing through the origin and having a slope of $\sqrt{\frac{g}{4 h}}$
It will be a straight line not passing through the origin

The correct answer is: It will be straight line passing through the origin and having a slope of $square root of fraction numerator g over denominator 8 h end fraction end root$

Assuming particle 2 to be at rest, substituting in
$y equals x tan invisible function application theta minus fraction numerator g x to the power of 2 end exponent over denominator 2 u to the power of 2 end exponent cos to the power of 2 end exponent invisible function application theta end fraction blank left parenthesis theta equals 0 degree right parenthesis$

We have $negative h equals fraction numerator negative g over denominator 2 left parenthesis 4 v to the power of 2 end exponent right parenthesis end fraction$
or $v equals square root of fraction numerator g over denominator 8 h end fraction end root$
Which is a straight line passing through origin with slope $square root of fraction numerator g over denominator 8 h end fraction end root$

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