A ball of mass rests on a vertical post of height . A bullet of mass , travelling in horizontal direction, hits the centre of the ball. After collision both travel independently. The ball hits the ground at a distance of and the bullet at a distance of from the foot of the post. The value of initial velocity of the bullet will be (if ):
Correct answer:D
Standard Method
Given: mass of ball , mass of bullet , height of post , horizontal distances are for the ball and for the bullet.
Find: the initial velocity of the bullet.
Both bodies start falling from the same height after collision, so their time of fall is the same.
Hence the horizontal speeds just after collision are obtained from distance speed time.
Using conservation of momentum in the horizontal direction:
Substituting the values into the formula, the final velocity is:
Therefore, the initial velocity of the bullet is . The correct option is D.
Using different times of fall for the ball and bullet. This is wrong because both start from the same height with zero initial vertical velocity after collision. Use the same for both bodies.
Applying conservation of momentum in the vertical direction. This is wrong because the collision and given motion data concern the horizontal direction. Use horizontal momentum conservation.
Forgetting to convert masses consistently before using momentum. This is wrong because momentum depends on mass ratios. Use a consistent unit system for both masses.
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