# Inelastic Football Collision Problem

• ryanx806
In summary, after the tackle, the halfback has a momentum of 684 kg*m/s in the +x direction and the opponent has a momentum of -288 kg*m/s in the -x direction. The final velocity and direction of the players is in the opposite direction of their original momentum.
ryanx806

## Homework Statement

A halfback with a mass m1=90kg is running up field with a speed of v1=7.6m/s. He is tackled by an opponent with a mass of m2=120kg, who approaches the halfback at an angle of 30 degrees with a velocity of v2=4.0m/s. Assume the collision is perfectly inelastic.

a) Calculate the magnitude and direction of the resultant velocity of the two players just after the tackle.

b) Calculate the change in kinetic energy (in Joules) for the system of the two players.

## Homework Equations

I'm confused about calculating the initial momentum of each of the players, and how to add them together to get the final velocity and direction.

## The Attempt at a Solution

Remember that momentum is a vector, so it has a magnitude and direction. Draw a sketch of the momenta before the collision. Let's orient the axes so that the halfback is running in the +x direction. You can represent his momentum as an arrow pointing to the right. How long should this arrow be? Which way should the arrow representing the opponent's momentum be? What is its magnitude?

To combine them, you have to add them vectorially. That means breaking them up into components and adding the respective components together.

1 person
My professor gave us an example that uses the equation for conservation of momentum (mvi=mvf), which I understand. But I'm confused on whether I need to solve this equation for both players in both axes (which would give me 2 final x-velocities and 2 final y-velocities) or if I just use the equation once to find a total final x- and y-velocity.

Does the "perfectly inelastic collision" part tell us anything important about the outcome?

So...

(90kg)(7.6m/s) + (120kg)(4m/s) = 1164kg*m/s

Does that mean that the final velocity = 1164/(90kg + 120kg) ?

And if so, how do I know which direction they are going after the collision?

I am sorry. I deleted the equation line I wrote because I realized it may be a little misleading.

You need to add them as vectors like vela explained. Letting the halfback's momentum be in the x(+ve) direction is a sensible place to start. Drawing out the vectors may be helpful too.

Eg. Halfback's momentum => (90)*(7.6) = 684
Therefore coordinates of this vector (starting from the origin) are:
x = 684
y = 0

Apply trigonometry (using the angle given in the problem) to the magnitude of the second vector to get its x and y components. Be sure to remember if the components have negative values. Eg if the opponent were running straight at the halfback, his x component would be negative because we set the halfbacks motion to be in the positive x direction.

Once you have x and y components for each players momentum vector, add the two x components, and the two y components. This will give you the x and y components of the final vector. From there you can use pythagorus and trig to get the magnitude and direction of the final congealed mass of tangled players, respectively.

1 person
Okay! Thank you so much! I think that's what I was originally trying to do, but my professor's example made me question it. I really appreciate your help though!

## 1. What is an inelastic football collision?

An inelastic football collision is a situation where two objects, in this case, footballs, collide and stick together after the collision instead of bouncing off each other. This means that the total kinetic energy of the system is not conserved, as some energy is lost in the form of heat and deformation of the objects.

## 2. How is the inelastic football collision problem relevant to scientific research?

The inelastic football collision problem is relevant to scientific research because it helps us understand the principles of conservation of momentum and energy. It also has applications in fields such as engineering, physics, and sports science, where understanding the dynamics of collisions is crucial.

## 3. What factors affect the outcome of an inelastic football collision?

The outcome of an inelastic football collision can be affected by factors such as the mass, velocity, and angle of the two colliding objects, as well as the material properties of the objects, such as their elasticity and surface texture.

## 4. How can the inelastic football collision problem be solved?

The inelastic football collision problem can be solved using principles of conservation of momentum and energy. This involves setting up equations to represent the initial and final states of the system and solving for the unknown variables, such as the final velocity or the amount of energy lost in the collision.

## 5. What are some real-life examples of inelastic football collisions?

Some real-life examples of inelastic football collisions include a car hitting a wall, a person catching a ball, or a hammer hitting a nail. These collisions may not be perfectly inelastic, but they demonstrate the concept of objects sticking together after a collision and energy being lost in the process.

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