# Air Track Elastic Collision: Solving for Final Velocities

In summary, the conversation discusses a problem involving two gliders on a frictionless air track and their head-on collision. The task is to find the final velocities of both gliders after the collision, given their initial velocities and the fact that the collision is elastic. The equations for conservation of kinetic energy and momentum are used to solve the problem, but the previous attempts at finding the final velocities were incorrect. The person asking for help is asked to show how they set up the equations and solved them.

## Homework Statement

A 0.159kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.870m/s . It has a head-on collision with a 0.310kg glider that is moving to the left with a speed of 2.15m/s . Suppose the collision is elastic.

a) Find the magnitude of the final velocity of the 0.159kg glider.

b) Find the magnitude of the final velocity of the 0.310kg glider.

## The Attempt at a Solution

I know that both the kinetic energy and the momentum is preserved, and I have "constructed" both the equations, but I can't get the right answer!

Here are my previous answers (which were wrong):
Part A:
2.1752
1.7161
1.1262
0.4295

Part B:
0.5899
0.4295
0.2

Thanks!

I know that both the kinetic energy and the momentum is preserved, and I have "constructed" both the equations, but I can't get the right answer!
Show how you set up the equations and how you solved them.

Here are my previous answers (which were wrong):
Part A:
2.1752
1.7161
1.1262
0.4295
Don't just give a list of answers. Show how you got them. That way we can see where you are going wrong.

## 1. What is an air glider elastic collision?

An air glider elastic collision is a type of collision that occurs when an object, typically a glider or airplane, collides with another object in the air. In this type of collision, both objects maintain their original shapes and velocities after impact. This is due to the elastic nature of the materials and forces involved.

## 2. How does an air glider elastic collision differ from other types of collisions?

In an air glider elastic collision, the objects involved do not lose any kinetic energy during the collision. This is in contrast to an inelastic collision, where the objects stick together and some kinetic energy is lost. Additionally, in an elastic collision, the objects maintain their original shape, while in a plastic collision, they are permanently deformed.

## 3. What factors can affect an air glider elastic collision?

The speed and angle of approach, as well as the elasticity and mass of the objects involved, can all affect the outcome of an air glider elastic collision. The air density and air resistance can also play a role in the collision.

## 4. How is the outcome of an air glider elastic collision calculated?

The outcome of an air glider elastic collision can be calculated using the principles of conservation of momentum and conservation of kinetic energy. These equations take into account the mass, velocity, and angle of approach of the objects before and after the collision.

## 5. What are some real-world applications of air glider elastic collisions?

Air glider elastic collisions are common in the field of aviation, particularly in air traffic control and accident investigation. They are also used in sports, such as in the design of golf clubs and tennis rackets, to optimize the transfer of kinetic energy. In addition, understanding elastic collisions is important in the development and testing of safety equipment, such as car airbags and helmets.

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