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An object flying in air with velocity (20i + 25j − 12k) suddenly breaks into two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity (100i + 35j + 8k). The velocity of the larger piece will be

1. −20i − 15j − 80k
2. 4i + 23j − 16k
3. −100i − 35j − 8k
4. 20i + 15j − 80k

Correct answer: 4i + 23j − 16k

Solution

Using conservation of momentum, the total momentum before and after the break must be equal. The initial momentum is the mass times velocity of the object. After the break, the momentum of the smaller and larger pieces is calculated using their respective masses and velocities. Solving for the velocity of the larger piece gives 4i + 23j − 16k.

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