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Suzy, Marie, Gabby, and Veronica are playing football in the park. Both Marie and Gabby go for the interception and crash into each other! If their total momentum is 382 kg. m/s after the collision and Marie's momentum is 180 kg . m/s before the collision, what is Gabby's momentum before the collision?

Respuesta :

Answer:

Gabby's momentum before the collision is 202 kgĀ·m/s

Explanation:

The given parameters of the motion of the people playing football in the park are;

The interaction of Marie and Gabby when they go for the interception = Collide

The total momentum of Marie ang Gabby after the collision, [tex]\Sigma P_{final}[/tex] = 382 kgĀ·m/s

The initial momentum of Marie, Pā‚ = 180 kgĀ·m/s

By the law conservation of conservation of linear momentum, we have;

The total initial momentum before the collision, [tex]\Sigma P_{initial}[/tex] = The total momentum after the collision, [tex]\Sigma P_{final}[/tex]

The total initial momentum before the collision, [tex]\Sigma P_{initial}[/tex] = Marie's momentum before the collision, Pā‚ + Gabby's momentum before the collision, Pā‚‚

āˆ“ [tex]\Sigma P_{initial}[/tex] = Pā‚ + Pā‚‚ = 180 kgĀ·m/s + Pā‚‚

From which we have;

[tex]\Sigma P_{initial}[/tex] = 180 kgĀ·m/s + Pā‚‚ = [tex]\Sigma P_{final}[/tex] = 382 kgĀ·m/s

āˆ“ 180 kgĀ·m/s + Pā‚‚ = 382 kgĀ·m/s

Pā‚‚ = 382 kgĀ·m/s - 180 kgĀ·m/s = 202 kgĀ·m/s

Pā‚‚ = 202 kgĀ·m/s

Gabby's momentum before the collision, Pā‚‚ = 202 kgĀ·m/s.

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