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BITSAT2015PhysicsMotion in Two DimensionsActual

A particle of mass 2 ~m is projected at an angle of 45^ with the horizontal with a velocity of 20 2 ~m / s . After 1 ~s , explosion takes place and the particle is broken into two equal pieces. As a result of explosion, one part comes to rest. The maximum height from the ground attained by the other part is

Options

  1. A50 ~m
  2. B25 ~m
  3. C40 ~m
  4. D35 ~m

Correct answer

D. 35 ~m

Step-by-step solution

Given : Initial velocity u₀=20 2 ~m / s ; angle of projection =45^ Therefore horizontal and vertical components of initial velocity are u _ x =20 2 45^ =20 ~m / s and u _ y =20 2 45^ =20 ~m / s After 1 ~s , horizontal component remains unchanged while the vertical component becomes v_ y =u_ y -g t Due to explosion, one part comes to rest. Hence, from the conservation of linear momentum, vertical component of second part will become v_ y ^ =20 m / s Therefore, maximum height attained by the second part will be H = h

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