Physics-
General
Easy

Question

A bullet fired into a fixed wooden block loses half of its velocity after penetration 40 cm. it comes to rest after penetrating a further distance of

  1. fraction numerator 22 over denominator 3 end fraction c m  
  2. fraction numerator 40 over denominator 3 end fraction c m  
  3. fraction numerator 20 over denominator 3 end fraction c m  
  4. fraction numerator 22 over denominator 5 end fraction c m  

The correct answer is: fraction numerator 40 over denominator 3 end fraction c m


    Let initial velocity of body a point A is v comma blank A B is 40 cm.
    From v to the power of 2 end exponent equals u to the power of 2 end exponent minus 2 a s
    rightwards double arrow blank open parentheses fraction numerator v over denominator 2 end fraction close parentheses to the power of 2 end exponent equals v to the power of 2 end exponent minus 2 a cross times 40
    O r blank a equals fraction numerator 3 v to the power of 2 end exponent over denominator 320 end fraction
    Let on penetrating 40 cm in a wooden block, the body moves x distance from B blank t o blank C.
    So, for B blank t o blank C
    u equals fraction numerator v over denominator 2 end fraction comma v equals 0
    s equals x comma blank a equals fraction numerator 3 v to the power of 2 end exponent over denominator 320 end fraction left parenthesis d e c e l e r a t i o n right parenthesis
    therefore blank open parentheses 0 close parentheses to the power of 2 end exponent equals open parentheses fraction numerator v over denominator 2 end fraction close parentheses to the power of 2 end exponent minus 2 cross times fraction numerator 3 v to the power of 2 end exponent over denominator 320 end fraction cross times x
    O r blank x equals fraction numerator 40 over denominator 3 end fraction c m

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