A 90.0-kg fullback running east with a speed of 5.00 m / s...

A $90.0-\mathrm{kg}$ fullback running east with a speed of $5.00 \mathrm{~m} / \mathrm{s}$ is tackled by a $95.0-\mathrm{kg}$ opponent running north with a speed of $3.00 \mathrm{~m} / \mathrm{s}$. If the collision is perfectly inelastic, (a) calculate the speed and direction of the players just after the tackle and (b) determine the energy lost as a result of the collision. Account for the missing energy.

A $90.0-\mathrm{kg}$ fullback running east with a speed of $5.00 \mathrm{~m} / \mathrm{s}$ is tackled by a $95.0-\mathrm{kg}$ opponent running north with a speed of $3.00 \mathrm{~m} / \mathrm{s}$. If the collision is perfectly inelastic,
(a) calculate the speed and direction of the players just after the tackle and (b) determine the energy lost as a result of the collision. Account for the missing energy.

Key Concepts

Momentum Conservation

Momentum conservation is the foundational principle stating that the total momentum of an isolated system remains unchanged regardless of the interactions between its components. In collisions, this means that the vector sum of the momenta of interacting bodies before the collision equals the vector sum after the collision, even if kinetic energy is not conserved.

Inelastic Collision

An inelastic collision is one in which the colliding objects stick together after impact, moving as a single body. Although momentum is conserved in such collisions, kinetic energy is not because some of the energy is transformed into other forms such as heat, sound, or deformation energy.

Kinetic Energy Loss

In collisions, particularly inelastic collisions, kinetic energy is often not conserved because part of it is dissipated into other forms of energy during processes like deformation, heat generation, or sound emission. This loss of kinetic energy differentiates inelastic collisions from elastic ones where both momentum and kinetic energy remain conserved.

Vector Decomposition

Vector decomposition involves breaking down a vector into components, usually along mutually perpendicular axes. This process is crucial in collision problems where objects are moving in different directions, as it allows the application of conservation laws separately along each axis (for example, handling eastward and northward components independently).

Transcript

0:00 Welcome.

00:01 Today we'll be talking about collisions and momentum.

00:04 So first, we know this collision is perfectly inelastic.

00:10 So therefore we know that once the two players crash into each other, they'll stay together with one final velocity.

00:23 So from there, we know we can draw a diagram of the problem and it'll look something like this.

00:31 What we're looking for is the final velocity of the players after getting tackled.

00:40 So to do that, in this case, because this is two -dimensional, it has an x and a y component, we'll have to find momentum in the x and momentum in the y.

00:53 So for part a, we will have, in the x direction, we'll have the mass of the first player and the velocity of the first player is equal to the total mass times the final velocity because this has an x component while the second player does not so that term would be zero so isolating for final velocity in the x will get the mass the momentum of the first player divided by the total mass of the two players and this will be 90 times 5 then divided by 185 and this will give us 2 .43 meters per second along the x so for the y we'll have the same thing just now instead it'll be the second player with a velocity in the y direction so we'll have mass two velocity two is equal to the total mass times v final in the y now we want to isolate for the v final in the y so we'll have the final y is equal to mass two velocity two divided by the total mass so we'll have 95 times 3 divided by 180 and this will give us 1 .5 4 meters per second in the why so now we can use the pythagorean theorem.

03:19 First we can draw a small diagram.

03:30 So we know this component is 2 .43 meters per second and we know this component is 1 .54 meters per second and east and north which is also y and x.

03:59 So from there we'll just use pythagorean theorem to find the value for this v final and then we'll use the tan inverse to find the value to find the value for this v final.

04:14 Find the angle of the velocity...

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