How to Correctly Calculate Velocity in a Two-Dimensional Elastic Collision?

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In summary, the conversation discusses a problem where two rolling golf balls of the same mass collide. The velocity of one ball is initially 2 m/s [E] and after the collision, the velocities of the balls are 2.49 m/s [62.8° North of West] and 2.37 m/s [69.2° South Of East]. The problem is to determine the magnitude and direction of the unknown velocity. The conversation includes calculations using the conservation of momentum and the Pythagorean theorem to solve for the unknown velocity. The correct answer is given as 3 m/s and moving W for the initial velocity of the other ball, while the individual's answer was 4.7 m/s [20
  • #1
PiRsq
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I have a problem with this question,

1. Two rolling golf balls of the same mass collide. The velocity of one ball is initially 2 m/s [E] After the collision, the velocities of the balls are 2.49 m/s [62.8° North of West] and 2.37 m/s [69.2° South Of East]. What are the magnitude and direction of the unknown velocity?

Basicall I did:

For x component:


V1 + V2 = V1'cos(180°-62.8°) + V2'cos(360°-69.2°)

I solved for V2

I did the same for the y component then I took the x and y component values and did the pythagoras theorem to get the angle and value...The value at the back of the book is 3 m/s and moving W for the initial velocity of the other ball...My answer was 4.7 m/s [20° South of West]

Whats my mistake?
 
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  • #2
You certainly have the right idea. If you show more work I might be able to tell you where the problem is.
 
  • #3
I've got two answers and one of them is at the back of book. How do I know which ball moves where?
 
  • #4
Are you assuming conservation of energy (perfectly elastic collision)? If so you can use V12+ V22= V1'2+ V2'2.
 
  • #5
Originally posted by HallsofIvy
Are you assuming conservation of energy (perfectly elastic collision)? If so you can use V12+ V22= V1'2+ V2'2.

It's not necessary here.
He's got two unknowns, and two equations from conservation of momentum. The only unknowns are the x and y components of one ball's inital velocity, and the other inital and both of the final velocities are given.
 
  • #6
Im assuming its a perfectly elastic collision since its two golf balls
 

FAQ: How to Correctly Calculate Velocity in a Two-Dimensional Elastic Collision?

What is two dimensional momentum?

Two dimensional momentum is a physical quantity that describes the motion of an object in two dimensions. It is the product of an object's mass and its velocity in both the x and y directions.

How is two dimensional momentum calculated?

To calculate two dimensional momentum, you must first determine the mass of the object and its velocity in both the x and y directions. Then, you can use the equation p = mv, where p is the momentum, m is the mass, and v is the velocity in each direction.

What is the conservation of two dimensional momentum?

The conservation of two dimensional momentum states that, in a closed system, the total momentum in the x direction is equal to the total momentum in the y direction. This means that the total momentum of the system will remain constant unless acted upon by an external force.

How does two dimensional momentum relate to collisions?

In collisions, two dimensional momentum is conserved. This means that the total momentum of the objects before and after the collision will be equal. This allows us to predict the motion of objects after a collision.

Can two dimensional momentum be negative?

Yes, two dimensional momentum can be negative. This typically occurs when an object is moving in the opposite direction of a chosen positive direction. It does not affect the conservation of momentum, as long as the negative and positive directions are consistent throughout the problem.

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