To find the common velocity of the two trolleys after the collision, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Given: Mass of the first trolley (m1) = 2 kg Initial velocity of the first trolley (v1) = 3 m/s Mass of the second trolley (m2) = 1 kg Initial velocity of the second trolley (v2) = 0 m/s (stationary)
Using the conservation of momentum:
Total momentum before collision = Total momentum after collision
(m1 * v1) + (m2 * v2) = (m1 + m2) * v_common
(2 kg * 3 m/s) + (1 kg * 0 m/s) = (2 kg + 1 kg) * v_common
(6 kg m/s) = (3 kg) * v_common
Dividing both sides by 3 kg:
v_common = (6 kg m/s) / (3 kg) v_common = 2 m/s
Therefore, the common velocity of the two trolleys after the collision is 2 m/s.