A 0.2 kg plastic ball moves with a velocity of 1.5 m/s. It collides with a second plastic ball of mass 1.8 kg, which is moving along the same line at a speed of 0.1 m/s. After the collision, both balls continue moving in the same, original direction. The speed of the 1.8 kg ball is 0.26 m/s. What is the new velocity of the 0.2 kg ball?

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To solve this problem, we can apply the principles of conservation of momentum and kinetic energy.

Conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:

m1u1 + m2u2 = m1v1 + m2v2

Where:
m1 and m2 are the masses of the objects (in this case, the two plastic balls)
u1 and u2 are the initial velocities of the objects
v1 and v2 are the final velocities of the objects

Using this equation, we can calculate the final velocity of the 0.2 kg plastic ball (v1).

Given:
m1 = 0.2 kg (mass of the 0.2 kg ball)
u1 = 1.5 m/s (initial velocity of the 0.2 kg ball)
m2 = 1.8 kg (mass of the 1.8 kg ball)
u2 = 0.1 m/s (initial velocity of the 1.8 kg ball)
v2 = 0.26 m/s (final velocity of the 1.8 kg ball)

Plugging in these values into the conservation of momentum equation, we get:

(0.2 kg)(1.5 m/s) + (1.8 kg)(0.1 m/s) = (0.2 kg)(v1) + (1.8 kg)(0.26 m/s)

0.3 + 0.18 = 0.2v1 + 0.468

0.48 = 0.2v1 + 0.468

0.48 - 0.468 = 0.2v1

0.012 = 0.2v1

Dividing both sides by 0.2, we find:

0.012 / 0.2 = v1

v1 = 0.06 m/s

Therefore, the new velocity of the 0.2 kg plastic ball after the collision is 0.06 m/s.