# Angle of Deflection in Elastic Collision

• StarWarsNerd
In summary, the problem is to determine the angle of deflection after an elastic collision between two objects of different masses. The initial mass, angle, and speed of both objects are known, and the desired output is the final angle. After consulting with colleagues, it was found that the solution involves using the slope between the position of the two objects and taking the arctan of that. Conservation of momentum also applies in this system.

#### StarWarsNerd

This is the problem I am looking to solve: given two objects of different mass, find the angle of deflection after an elastic collision for each object.

For both objects we know:
• m : Mass in Kilograms
• θi : Initial Angle in Degrees
• si : Initial Speed in Units per Second
• sf : Final Speed in Units per Second
Looking For:
• θf : Final Angle in Degrees
I have asked some of my colleagues at work how to do this without assuming one of the objects is stationary, and no one knew how, so I am curious if there is a formula or a way to derive the angle from this information.

SOLVED: I guess it is as simple as getting the slope from the position of the two objects then taking the arctan of that.

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Conservation of momentum with the 2 objects applies since there is no net force in this system of 2 objects. Can you go from there?

## 1. What is the angle of deflection in an elastic collision?

The angle of deflection in an elastic collision is the angle at which two objects, typically spheres, change direction after colliding. It is the angle formed between the initial and final velocities of the objects.

## 2. How is the angle of deflection calculated?

The angle of deflection can be calculated using the law of conservation of momentum and the law of conservation of kinetic energy. This involves finding the initial and final velocities of the objects and using trigonometric functions to determine the angle.

## 3. Does the mass of the objects affect the angle of deflection?

Yes, the mass of the objects does affect the angle of deflection in an elastic collision. Objects with larger masses will have a smaller angle of deflection compared to objects with smaller masses, assuming all other factors remain constant.

## 4. What is the difference between elastic and inelastic collisions?

In an elastic collision, both the kinetic energy and momentum of the objects are conserved. This means that the objects bounce off each other without any loss of energy or deformation. In an inelastic collision, some of the energy is lost and the objects may deform upon impact.

## 5. Can the angle of deflection be greater than 90 degrees?

Yes, the angle of deflection can be greater than 90 degrees in certain situations. This would occur when the objects have initial velocities that are not directly towards each other, causing them to change direction and have a final velocity that is perpendicular to the initial velocity.