Question

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?

Answer 1

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

Step-by-step 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,
`\Sigma P_(final)` = 382 kg·m/s

The initial momentum of Marie, P₁ = 180 kg·m/s

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

The total initial momentum before the collision,
`\Sigma P_(initial)` = The total momentum after the collision,
`\Sigma P_(final)`

The total initial momentum before the collision,
`\Sigma P_(initial)` = Marie's momentum before the collision, P₁ + Gabby's momentum before the collision, P₂

∴
`\Sigma P_(initial)` = P₁ + P₂ = 180 kg·m/s + P₂

From which we have;

`\Sigma P_(initial)` = 180 kg·m/s + P₂ =
`\Sigma P_(final)` = 382 kg·m/s

∴ 180 kg·m/s + P₂ = 382 kg·m/s

P₂ = 382 kg·m/s - 180 kg·m/s = 202 kg·m/s

P₂ = 202 kg·m/s

Gabby's momentum before the collision, P₂ = 202 kg·m/s.