An oxygen atom (mass 16 u) moving at 733 m/s at 15.0^/circ15.0 ∘ with respect to the / hat{i} i ^ direction collides and sticks to an oxygen molecule (mass 32 u) moving at 528 m/s at 128^/circ128 ∘ with respect to the / hat{i} i ^ direction. The two stick together to form ozone. What is the direction of the final velocity of the ozone molecule?

Question

Physics

Punk

12 September, 13:07

An oxygen atom (mass 16 u) moving at 733 m/s at 15.0^/circ15.0 ∘ with respect to the / hat{i} i ^ direction collides and sticks to an oxygen molecule (mass 32 u) moving at 528 m/s at 128^/circ128 ∘ with respect to the / hat{i} i ^ direction. The two stick together to form ozone. What is the direction of the final velocity of the ozone molecule?

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Rachel Norris · Answer 1

Representing the velocity of oxygen atom in vector form

v₁ = 733 cos 15 i + 733 sin15 j

= 708 i + 189.7 j

Similarly velocity of oxygen molecule

= 528 cos 128 i + 528 sin128 j

= - 325 i + 416 j

Applying conservation of momentum

m₁ v₁ + m₂v₂ = (m₁ + m₂) v

16 (708 i + 189.7 j) + 32 (-325 i + 416 j) = 48 v

11328 i + 3035.2 j - 10400 i + 13312 j = 48 v

928 i + 16347.2 j = 48 v

v = 19.33 i + 340.56 j

angle of this vector

tanθ = 340.56 / 19.33

= 17.61

87 °