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Question

A bullet of mass m is fired with a velocity of 50 m s to the power of negative 1 end exponent at an angle theta with the horizontal. At the highest point of its trajectory, it collides had on with a bob of massless string of length l equals 10 divided by 3m and gets embedded in the bob. After the collision, the string moves to an angle of 120degree. What is the angle theta ?

  1. cos to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 4 over denominator 5 end fraction close parentheses    
  2. cos to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 5 over denominator 4 end fraction close parentheses    
  3. sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 4 over denominator 5 end fraction close parentheses    
  4. sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 5 over denominator 4 end fraction close parentheses    

The correct answer is: cos to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 4 over denominator 5 end fraction close parentheses


    Velocity of bullet at highest point of its trajectory = 50 cos invisible function application theta in horizontal direction.
    As bullet of mass m collides with pendulum bob of mass 3m and two stick together, their common velocity
    v to the power of ´ end exponent equals fraction numerator m subscript 1 end subscript 50 cos invisible function application theta over denominator m plus 3 n end fraction equals fraction numerator 25 over denominator 2 end fraction cos invisible function application theta m s to the power of negative 1 end exponent
    As now under this velocity v ´ pendulum bob goes up to an angel 120degree, hence
    fraction numerator v to the power of ´ 2 end exponent over denominator 2 g end fraction equals h equals l open parentheses 1 minus cos invisible function application 120 degree close parentheses equals fraction numerator 10 over denominator 3 end fraction open square brackets 1 minus open parentheses f minus fraction numerator 1 over denominator 2 end fraction close parentheses close square brackets equals 5
    rightwards double arrow blank v to the power of ´ 2 end exponent equals 2 cross times 10 cross times 5 equals 100 or v to the power of ´ end exponent equals 10
    Comparing two answer of v ´, we get
    fraction numerator 25 over denominator 2 end fraction cos invisible function application theta equals 10 rightwards double arrow cos invisible function application theta equals fraction numerator 4 over denominator 5 end fraction ortheta equals cos to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 4 over denominator 5 end fraction close parentheses

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