Consider the head-on collision between a nitrogen molecule, mass 28u and a water molecule mass 18u. Prior to the collision, the nitrogen molecule is moving with velocity 0.4390 km/s and the water molecule is moving with velocity -0.7690 km/s. Positive velocities indicate a molecule moving to the right and a negative velocities indicate a molecule moving to the left. Immediately after the collision, the velocity of the water molecule is v = 0.7016 km/s. The atomic mass unit (u) is commonly used to indicate the mass of atoms and molecules: 1u=1.66×10-27kg. What is the velocity of the nitrogen molecule immediately after the collision? (in km/s)

When there is no external force acting on the system, the initial momentum before collision is equal to the final momentum after collision.

According to the momentum conservation principle,

m₁u₁ +m₂u₂ =m₁v₁ +m₂v₂

here, u represents the initial velocities, v represents final velocities and m represents the masses.

Given is the mass of nitrogen molecule, m₁ =28u =28 x 1.66×10⁻²⁷kg = 46.48 x 10⁻²⁷kg

the mass of water molecule, m₂ =18u =18 x 1.66×10⁻²⁷kg = 29.88 x 10⁻²⁷kg

initial velocity of nitrogen molecule u₁ = 0.4390 km/s

initial velocity of water molecule u₂ = -0.7690 km/s

final velocity of water molecule v₂ = 0.7016 km/s

Substituting the values into the above expression, we get the final velocity of the nitrogen molecule

46.48 x 10⁻²⁷kg x 0.4390 km/s + 29.88 x 10⁻²⁷kg x (-0.7690 km/s) = 46.48 x 10⁻²⁷kg x v₁ + 29.88 x 10⁻²⁷kg x 0.7016 km/s

v₁ = -0.5064 km/s

Thus, the final velocity of nitrogen molecule is -0.5064 km/s (to left).

Learn more about conservation of linear momentum.

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