Conservation of Momentum, a Totally Inelastic Collision

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SUMMARY

The discussion focuses on solving a problem involving the conservation of momentum in a totally inelastic collision between a 950kg compact car and a 450kg hay wagon. The initial velocities are given as ⃗v1 = 32 ˆx + 17 ˆy m/s for the car and ⃗v2 = 12 ˆx + 14 ˆy m/s for the wagon. The correct approach involves separately calculating the momentum in the x and y components using the formula m1v1 + m2v2 = (m1 + m2)vf. The solution requires adding the x-components and y-components of the velocities before applying the conservation of momentum equation.

PREREQUISITES
  • Understanding of vector components in physics
  • Knowledge of conservation of momentum principles
  • Familiarity with totally inelastic collisions
  • Basic algebra for solving equations
NEXT STEPS
  • Study vector addition in physics, focusing on components
  • Learn about totally inelastic collisions and their characteristics
  • Practice problems involving conservation of momentum with different masses
  • Explore the implications of frictionless surfaces in collision scenarios
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Students studying physics, particularly those focusing on mechanics and collision theory, as well as educators looking for practical examples of momentum conservation in inelastic collisions.

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Homework Statement



A 950kg compact car is moving with the velocity ⃗v1 = 32 ˆx + 17 ˆy m/s. It
skids on an icy, frictionless patch and collides with a 450kg hay wagon
moving with velocity ⃗v2 = 12ˆx +14ˆy m/s. If the two stay together,
what is their velocity?


Homework Equations



m1v1 (initial) + m2v2 (initial) = vf (m1+ m2)

The Attempt at a Solution



I realize this is a totally inelastic collision and I need to use the above equation to solve. However, I don't know how to change the vector components into a number that can be plugged into the formula. I have tried adding the vector components of both velocities (x+x, y+y) but the answers I am getting do not sound right. I tried doing this because I figured if I know the numbers for the masses I can factor them out and have the vectors being added to together, but I don't think this is the solution. Please help!
 
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Show your calculations. Try this one.
m1*v1x + m2*v2x = (m1+m2)*vfx.
Similarly for y components.
 

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