Physics-
General
Easy

Question

A bullet fired into a fixed target loses half of its velocity after penetrating 3 blank c m. How much further it will penetrate before coming to rest assuming that if faces constant resistance to motion

  1. 1.5 blank c m  
  2. 1.0 blank c m  
  3. 3.0 blank c m  
  4. 2.0 blank c m  

The correct answer is: 1.0 blank c m


    Let initial velocity of the bullet equals u
    After penetrating 3 blank c m its velocity becomes fraction numerator u over denominator 2 end fraction

    From v to the power of 2 end exponent equals u to the power of 2 end exponent minus 2 a s
    open parentheses fraction numerator u over denominator 2 end fraction close parentheses to the power of 2 end exponent equals u to the power of 2 end exponent minus 2 a left parenthesis 3 right parenthesis
    rightwards double arrow 6 a equals fraction numerator 3 u to the power of 2 end exponent over denominator 4 end fraction rightwards double arrow a equals fraction numerator u to the power of 2 end exponent over denominator 8 end fraction
    Let further it will penetrate through distance x and stops at point C
    For distance B C comma blank v equals 0 comma u equals u divided by 2 comma blank s equals x comma a equals u to the power of 2 end exponent divided by 8
    For v to the power of 2 end exponent equals u to the power of 2 end exponent minus 2 a s rightwards double arrow 0 equals open parentheses fraction numerator u over denominator 2 end fraction close parentheses to the power of 2 end exponent minus 2 open parentheses fraction numerator u to the power of 2 end exponent over denominator 8 end fraction close parentheses. x rightwards double arrow x equals 1 blank c m

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