How Fast Was Kevin Skating Before the Inelastic Collision?

[agadag]

Homework Statement

Kevin has a mass of 84.2 kg and is skating with in-line skates. He sees his 23.2-kg younger brother up ahead standing on the sidewalk, with his back turned. Coming up from behind, he grabs his brother and rolls off at a speed of 1.74m/s. Ignoring friction, find Kevin's speed just before he grabbed his brother.

Homework Equations

V= d/t ?
I have no idea how to solve this eqn!
The only eqn i have for perfectly inelastic collision involves center of mass.

PLEASE HELP!

 

[sylas]

Homework Statement

Kevin has a mass of 84.2 kg and is skating with in-line skates. He sees his 23.2-kg younger brother up ahead standing on the sidewalk, with his back turned. Coming up from behind, he grabs his brother and rolls off at a speed of 1.74m/s. Ignoring friction, find Kevin's speed just before he grabbed his brother.

Homework Equations

V= d/t ?
I have no idea how to solve this eqn!
The only eqn i have for perfectly inelastic collision involves center of mass.

PLEASE HELP!

In an inelastic collision, kinetic energy is lost, but momentum is still conserved. Use conservation of momentum.

 

[tomcue]

Hello Kevin, thank you for your question. I am happy to provide you with an explanation of the concept of perfectly inelastic collision and how it applies to your scenario.

First, let's define what a perfectly inelastic collision is. It is a type of collision where two objects collide and stick together after the collision, resulting in a loss of kinetic energy. This means that the final velocity of the two objects after the collision is the same.

In your scenario, Kevin is skating with a speed of 1.74 m/s and his brother is standing still. When Kevin grabs his brother, the two objects stick together and roll off at the same speed of 1.74 m/s. This is a perfectly inelastic collision because the two objects have become one and there is a loss of kinetic energy.

To find Kevin's speed just before he grabbed his brother, we can use the conservation of momentum principle. This principle states that the total momentum before a collision is equal to the total momentum after the collision. In this case, the total momentum before the collision is equal to the mass of Kevin (84.2 kg) multiplied by his initial velocity (V) and the total momentum after the collision is equal to the combined mass of Kevin and his brother (84.2 kg + 23.2 kg) multiplied by their final velocity (1.74 m/s).

Mathematically, this can be represented as:

84.2 kg * V = (84.2 kg + 23.2 kg) * 1.74 m/s

Solving for V, we get:

V = (84.2 kg + 23.2 kg) * 1.74 m/s / 84.2 kg

V = 1.74 m/s * (107.4 kg / 84.2 kg)

V = 1.74 m/s * 1.276

V = 2.22 m/s

Therefore, Kevin's speed just before he grabbed his brother was 2.22 m/s.

I hope this explanation helps you understand the concept of perfectly inelastic collision and how it applies to your scenario. Let me know if you have any further questions. Keep up the good work in your studies!