A block of mass 3 kg is moving with a velocity of 6 m/s on a frictionless horizontal surface. It explodes into two pieces. One piece of mass 1 kg moves with a velocity of 10 m/s in the original direct

Question

A block of mass 3 kg is moving with a velocity of 6 m/s on a frictionless horizontal surface. It explodes into two pieces. One piece of mass 1 kg moves with a velocity of 10 m/s in the original direction. Find the speed of the other piece in m/s.

TestHub · Accepted Answer

According to the principle of conservation of momentum, the total momentum of the system before the explosion must be equal to the total momentum after the explosion, as there are no external forces. Initial momentum $P_{ini t ia l} = M V = 3 k g \times 6 m / s = 18 k g \cdot m / s$ .

After the explosion, let $m_{1} = 1 k g$ and $v_{1} = 10 m / s$ . The mass of the second piece is $m_{2} = M - m_{1} = 3 - 1 = 2 k g$ . Let its velocity be $v_{2}$ . By conservation of momentum: $P_{ini t ia l} = m_{1} v_{1} + m_{2} v_{2}$ . $18 = (1) (10) + (2) v_{2} ⟹ 18 = 10 + 2 v_{2} ⟹ 8 = 2 v_{2} ⟹ v_{2} = 4 m / s$

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