Which car was going faster before the collision? Solving for momentum in 2D

In summary, a grade 12 Physics class was given a basic assignment to think outside the box of typical questions. The question was about two cars of identical mass colliding at an intersection and moving away at an angle of [East 22 degrees North]. With limited information, the student struggled to solve the problem using algebra but eventually realized that breaking the final velocity into components and relating them to the initial conditions would help. The challenge of connecting concepts and equations is a common difficulty in physics and science.
  • #1
Stevo191
2
0
So we've just finished our unit on Momentum and Energy in our grade 12 Physics class and today we were given a basic assignment that is to help us think "out-side" the box of typical questions. This particular question has me going insane...I just can't make the connection as to what to do.

The question is:

Two cars of identical mass are approaching the same intersection, one from the south and one from the west. They reach the intersection at the same time and collide. The cars lock together and move away at an angle of [East 22 degrees North]. Which car was going faster before the collision? Explain your reasoning and include all calculations.

Normally with a question like this, I'd be fine trying to solve it with all of the given variables and such (Using the m1v1i + m2v2i = m1v1f + m2v2f equation), but since this gives almost no information, I am at a loss as to how to solve it. Using logic, I know that the car traveling to the east is the one traveling faster since the final vector is going 68 degrees east, while only going 22 degrees north. How do I answer that using algebra with so little specific information? Any sort of help to point me in the right direction would be awesome...
 
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  • #2
Try breaking up the final velocity into components. How can you relate them to the whole / each other? How does that relate to the initial conditions?
 
  • #3
Ahhh yes. That would make sense...I should have thought of that. :\

Thanks, I'll give it a go. :)
 
  • #4
I think one of the hardest parts of physics (and science in general) is making the connection / transition between the concepts and the equations. I'd say, most people can do one OR the other; either the math, or the ideas - but its a lot harder to be able to combine the two, and find one from the other.

Good luck, Cheers!
 

1. What is momentum in 2D?

Momentum in 2D refers to the quantity of motion an object has in a two-dimensional space. It is a vector quantity, meaning it has both magnitude and direction.

2. How is momentum calculated in 2D?

In 2D, momentum is calculated by multiplying the mass of an object by its velocity in the x and y directions. This can be represented by the equation: p = m * v, where p is momentum, m is mass, and v is velocity.

3. What is the difference between momentum and velocity?

While momentum and velocity are both related to an object's motion, they are slightly different. Velocity is the rate of change of an object's position, while momentum is the product of an object's mass and velocity. In other words, velocity describes how fast an object is moving, while momentum describes how difficult it is to stop the object's motion.

4. How does momentum behave in a 2D collision?

In a 2D collision, momentum is conserved, meaning that the total momentum of the system before the collision is equal to the total momentum after the collision. This means that the sum of the momentum in the x and y directions remains constant, even if the individual momenta of the objects involved change.

5. What are some real-life examples of momentum in 2D?

Some real-life examples of momentum in 2D include billiard balls colliding on a pool table, two cars colliding at an intersection, or a person jumping from a diving board into a pool. In all of these scenarios, momentum is conserved and can be calculated using the mass and velocity of the objects involved.

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