# Inelastic collisions in 2 dimensions

• SohailS
In summary, the problem is asking for the final velocity of a target after an inelastic collision with an arrow. The initial velocities of the two objects are given and the equations used to solve the problem are provided. However, the problem does not specify if the collision is completely inelastic or not, so it is assumed to be completely inelastic.
SohailS
I am unsure how to proceed with this problem because it is asking for the final velocity of one of the two objects given the initial velocities. This is an inelastic collision not a completely inelastic collision, which means the two objects do not stick together. The book makes a distinction between the two.

If you can give me some hints as how to proceed it would be truly helpful.

## Homework Statement

A 0.800 kg target slides along the ice at 3.0 m/s [W], when it is hit by a 20.0 g arrow
moving at 260 m/s [N], as part of a show. Find the final velocity of the target after the
inelastic collision.

Given:

let east and north be positive

m1 = 0.800 kg
v1 = 3.0 m/s [W]
m2 = 0.0200 kg
v2 = 260 m/s [N]

find v1f

## Homework Equations

Pti=Ptf

m1v1i + m2v2i = m1v1f + m2v2f

## The Attempt at a Solution

The question is asking for the final velocity of the target which is find v1f
This is an inelastic collision, not a completely inelastic collision, this means the arrow will not stick to the target.

vix = -3.0 m/s
viy = 260 m/s

Pxi=(0.8)(-3)=-2.4 Ns
Pyi=(0.02)(260)=5.2 Ns

Last edited:
Hello.

If the arrow does not stick to the target, then there is not enough information to solve the problem. I suspect that even though the problem does not say completely inelastic, that is what you should assume (unless other information is given).

## 1. What is an inelastic collision in 2 dimensions?

An inelastic collision in 2 dimensions is a type of collision where the kinetic energy of the system is not conserved. This means that some of the initial kinetic energy is lost during the collision and is converted into other forms of energy, such as heat or sound.

## 2. How is momentum conserved in an inelastic collision in 2 dimensions?

In an inelastic collision in 2 dimensions, momentum is conserved just as it is in any other collision. This means that the total momentum before the collision is equal to the total momentum after the collision. However, unlike in elastic collisions where kinetic energy is also conserved, in inelastic collisions, some of the initial kinetic energy is converted into other forms of energy.

## 3. What factors affect the amount of energy lost in an inelastic collision in 2 dimensions?

The amount of energy lost in an inelastic collision in 2 dimensions depends on several factors such as the masses of the objects involved, the velocities before and after the collision, and the nature of the collision (e.g. whether it is a head-on collision or a glancing collision).

## 4. How is the coefficient of restitution used in inelastic collisions in 2 dimensions?

The coefficient of restitution is a measure of the elasticity of a collision. In inelastic collisions in 2 dimensions, the coefficient of restitution is less than 1, indicating that the objects do not bounce off each other and some of the initial kinetic energy is lost. This coefficient can be used to calculate the amount of energy lost in the collision.

## 5. What are some real-world examples of inelastic collisions in 2 dimensions?

Inelastic collisions in 2 dimensions occur in many real-world situations, such as car crashes, billiard ball collisions, and sports like hockey and soccer. In these scenarios, some of the initial kinetic energy is lost due to friction and deformation of the objects involved in the collision.

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