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# Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2 m/s and 1 m/s, respectively. They collide and after the collision, the first object moves at a velocity of 1.67 m/s. Determine the velocity of the second object.

Assuming that the first object is object A and the second one is object B, it is given that:

Mass of A (m1) = 100g

Mass of B (m2) = 200g

Initial velocity of A (u1) = 2 m/s

Initial velocity of B (u2) = 1 m/s

Final velocity of A (v1) = 1.67 m/s

Final velocity of B (v2) =?

Total initial momentum = Initial momentum of A + initial momentum of B

= m1u1 + m2u2

= (100) × (2) + (200) × (1) = 400 gm/sec

As per the law of conservation of momentum, the total momentum before collision must be equal to the total momentum post collision.

$$\therefore m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 = 400$$

$$\Rightarrow (100)(1.67) + (200)v_2 = 400$$

$$\therefore v_2 = \frac{400-167}{200} = 1.165 m/s$$