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

  1. It will be a parabola passing through the origin    
  2. 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    
  3. It will be a straight line passing through the origin and having a slope of square root of fraction numerator g over denominator 4 h end fraction end root    
  4. 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 slopesquare root of fraction numerator g over denominator 8 h end fraction end root

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