A $10 \mathrm{~kg}$ bomb is moving NORTH with a velocity of $4.0 \mathrm{~m} / \mathrm{s}$. It explodes into three fragments: a $5.0 \mathrm{~kg}$ fragment moving WEST with a speed of $8.0 \mathrm{~m} / \mathrm{s}$, a $4.0 \mathrm{~kg}$ fragment moving EAST with a speed of $10 \mathrm{~m} / \mathrm{s}$, and a third $1.0 \mathrm{~kg}$ fragment. What is the velocity of the third fragment?
A) $40 \mathrm{~m} / \mathrm{s} \mathrm{NORTH}$
B) $40 \mathrm{~m} / \mathrm{s}$ SOUTH
C) zero
D) none of these answers are correct

Question

Quizplus · Accepted Answer

Momentum is conserved in the explosion. The total momentum before the explosion is $10 \mathrm{~kg} \times 4.0 \mathrm{~m} / \mathrm{s} = 40 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ NORTH. The total momentum after the explosion is $5.0 \mathrm{~kg} \times 8.0 \mathrm{~m} / \mathrm{s} = 40 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ WEST, $4.0 \mathrm{~kg} \times 10 \mathrm{~m} / \mathrm{s} = 40 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ EAST, and the momentum of the third fragment. The momentum of the third fragment must be $40 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}$ NORTH to conserve momentum.

A 10 kg10 \mathrm{~kg}10 kg Bomb Is Moving NORTH with a Velocity Of 4.0 m/s4.0 \mathrm{~m} / \mathrm{s}4.0 m/s

A $10 \mathrm{~kg}$ Bomb Is Moving NORTH with a Velocity Of $4.0 \mathrm{~m} / \mathrm{s}$