# One and Two Dimension collisions

• clippers0319
In summary, the conversation is about solving for the final velocities of two balls after a collision on a frictionless table. The first part (a) is an elastic collision and the second part (b) is a completely inelastic collision. The solution involves using the conservation of kinetic energy and momentum equations to find the final velocities, and a helpful online resource is suggested for further understanding.
clippers0319
My question is not so much what to do it is just i have problems solving for a certain equation.

A 5.00kg ball, moving to the right at a velocity of 2m/s on a frictionless table, collides head-on with a stationary 7.50kg ball. Find the final velocities of the balls if the collision is (a) elastic and (b) completely inelastic

for part A

I have m1v1f + m2v2f= m1vi1 +0
to solve for final velocity 1(the ball for 5kg) you use

vf1=(m1-m2/m1+m2)vi1

I really have no i do how to algebraically solve for vf1, can someone explain that to me because when i use the equation i get the right answer which is -.400m/s

To find vf2 we use the fact that it is an ellastic collision and the kinetic energy before and after is the same

1/2m1(vf1^2)+1/2m2(vf2^2)=1/2m1(vi1^2)+0
Using this i have to solve for vf2 but again i have a problem algebraically solving for vf2. But there is a similar example in the textbook so i used what they had to solve for vf1 and vf2 but they do not show the work

vf2=(2m1/m1+m2)vi1

Same problem here but the answers come out correctly.
It would be greatly appreciated if someone can show me the algebra behind this

For (a): use the fact that both kinetic energy and momentum are conserved. This will give you two equations with two unknowns, which are the final velocities.

For (b): what are the properties of a completely inelastic collision?

I understand that but i need someone to show me how to algebraically solve for those two equations that's what my problem is i understand how to solve for the final velocities. Like show the math workout step by step because i am confused.

clippers0319 said:
I understand that but i need someone to show me how to algebraically solve for those two equations that's what my problem is i understand how to solve for the final velocities. Like show the math workout step by step because i am confused.

Here, take a look at: http://www.webmath.com/solver2.html" .

Last edited by a moderator:

## 1. What is a one-dimensional collision?

A one-dimensional collision is a type of collision in which the objects involved move along a straight line and have no rotation. This type of collision can be described using only one coordinate axis.

## 2. What is a two-dimensional collision?

A two-dimensional collision is a type of collision in which the objects involved move in a two-dimensional plane and may also have rotation. This type of collision requires the use of two coordinate axes to describe the motion of the objects.

## 3. What is the difference between an elastic and an inelastic collision?

In an elastic collision, both kinetic energy and momentum are conserved. This means that the total energy and momentum of the objects before and after the collision remain the same. In an inelastic collision, some kinetic energy is lost during the collision, usually in the form of heat or sound. Momentum is still conserved, but the total energy of the system decreases.

## 4. How do you calculate the final velocities of objects in a one or two-dimensional collision?

To calculate the final velocities of objects in a collision, you can use the conservation of momentum and energy equations. In a one-dimensional collision, momentum is conserved along the single axis, and in a two-dimensional collision, momentum is conserved along both axes. The equations can be solved simultaneously to find the final velocities of the objects.

## 5. What real-life examples can demonstrate one and two-dimensional collisions?

One-dimensional collisions can be seen in sports such as billiards, where the balls move in a straight line and collide with each other. Two-dimensional collisions can be seen in car crashes, where the cars can have both linear and rotational motion. Another example is a game of pool, where the balls can collide in both one and two dimensions.

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