# Ball collides with an inclined plane

1. Dec 1, 2006

### hannibalisfun

A ball mass m falls from height h and collides elastically with a frictionless inclined plane; the plane is a 45 degree angle with the horizontal. The first spot it collides with is p1 and then it bounces and collides with the plane again at p2. I think the ball bounce off the inclined plane at p1 in such a way that the velocity is parallel to the horizontal but this based on the diagram. So if someone could confirm this that would be much help

This is a 4 part problem. The first part I find at what speed the ball collides with the plane at p1. The next one and one I can’t figure out is how much time passes between p1 and p2. The next one is the distance between p1 and p2. I just found the horizontal length between p1 and p2 and divided by the velocity in part 1 because I think just after the collision all of the velocity was directed on the in the x direction. The last part is finding out the velocity of the ball at p2. The way I did this was I found out the vertical distance between p1 and p2 then found the gravitation potential energy between the two points and then set that equal to kinetic energy and found the velocity form need for them to be equal. Then I used Pythagorean Theorem to with legs being the velocity I found to the hypotenuse being the resultant vector.

2. Dec 1, 2006

### arildno

What you need to do, is to set up a list of what you need to find out, what you know, and finally, what relations held between known and unknown quantities.
THEN, you may attempt to solve the problem:

LIST OF WHAT YOU NEED TO FIND OUT:
1. Velocity of ball as it hits P1, let's call this quantity $$\vec{v}_{0}$$
2. Velocity of ball as it leaves P1, let's call this quantity $$\vec{v}_{1}$$
3. Time&distance from P1 to P2, let's call these quantities $$t_{1,2},d_{1,2}$$

Now, what are the quantities that are known to you that might be of help?
1. The ball's mass: m
2. Initial height: h
3. The ball FELL from its initial height.
4. The plane is frictionless
5. The angle is 45 degrees to the horizontal
6. We have an ELASTIC collision.

Now, what relations do we have to work with:
1. Newton's laws of motion!!!
Thus, we'll need to find laws of force appropriate to the problem:
a) Gravity
b) Normal force from the plane
Are there any others?

Possibly, the problem might be simplified by energy conservation arguments, collision theory, or the like.
For example, can we utilize the kinematic relations we know must hold when the acceleration is constant? (That is, can we find out if the acceleration is constant during some time periods?)

Last edited: Dec 1, 2006
3. Dec 1, 2006

### arildno

Now, try to set up appropriate equations in which your unkowns appear!