# Solving for Ball Collision: A vs. B Atop a Building

• kidia
A and B, being dropped and thrown from different heights. The collision between the two balls occurs at a certain fraction of the building's height, with ball A moving 4 times faster than ball B. Jameson is advised to use kinematic equations and the equation for kinetic energy to solve the problem. In summary, Jameson is seeking assistance with a physics problem involving two balls colliding at a fraction of a building's height, with one ball moving 4 times faster than the other. Suggestions are given to use kinematic equations and the equation for kinetic energy to solve the problem.
kidia
Does anyone can help me on this please?
Ball A is dropped from the top of building at the same instant the ball B is thrown vertically upward from the ground.When the balls collide,they are moving in the same direction,and the speed of A is 4 times that of B.At what fraction of the height of the building does collision occurs?
I will appreciate.

Think of ways to express the paths of both balls. Maybe a kinematic equation could help or perhaps the useful K.E. equation... $$K.E. = \frac{1}{2}mv^2$$

That should get you started.

Jameson

## 1. How do you calculate the velocity of the balls in a collision?

In order to calculate the velocity of the balls in a collision, you will need to know the mass of each ball, the initial velocity of each ball, and the coefficient of restitution (COR) of the surface they are colliding on. Using the formula v = u + COR(u'), where v is the final velocity, u is the initial velocity, and u' is the initial velocity of the other ball, you can calculate the final velocity of each ball.

## 2. How does the height of the building affect the collision of the balls?

The height of the building will affect the collision of the balls by changing the initial velocity of the balls. The higher the building, the longer the balls have to accelerate before reaching the ground. This will result in a higher initial velocity, which will affect the final velocity and outcome of the collision.

## 3. What factors affect the coefficient of restitution (COR) of the surface?

The coefficient of restitution (COR) of a surface is affected by the material and texture of the surface, as well as the temperature and humidity. Different surfaces will have different COR values, which can affect the outcome of the collision between the balls.

## 4. Can you predict the outcome of a collision between two balls based on their initial velocities and COR?

Yes, the outcome of a collision between two balls can be predicted by using the formula v = u + COR(u'), where v is the final velocity and u and u' are the initial velocities of the balls. By plugging in the known values, you can calculate the final velocity and determine if the balls will bounce off each other or stick together.

## 5. Is there a limit to the number of balls that can be involved in a collision on top of a building?

There is no set limit to the number of balls that can be involved in a collision on top of a building. However, as the number of balls increases, the complexity of the collision and the calculations involved also increase. Additionally, the size and strength of the building may also play a role in how many balls can safely collide on top of it.

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