Ball bounce angle on inclined surface

[Faris Shajahan]

Homework Statement

Ball strikes inclined plane of infinite mass with velocity v vertically. Elastic collisions. Velocity and direction after collision?

One way of solving is take components along and perpendicular to inclined plane and then solve easily.

Is there any way to solve is using energy conservation or some other way?

Homework Equations

Irrelevant. ;)

The Attempt at a Solution

The collision attempt (rather the solution):
Component ##\frac{v}{\sqrt{2}}## and ##\frac{v}{\sqrt{2}}##.
One component reversed, other the same.
Hence answer velocity v horizontally.

P.S.: This is NOT a homework question but for some reason the site admins don't accept that!

 

[RUber]

What other methods did you have in mind?
Are you looking for a more general method that will work for different angles, inelastic collisions, etc.?
Conservation of energy is in effect in your method since ##\| v_{in}\| = \| v_{out}\|##

 

[Faris Shajahan]

What other methods did you have in mind?
Are you looking for a more general method that will work for different angles, inelastic collisions, etc.?

I don't care. Just any other method other than the one I used. And I am kind of looking for a "not collision" method.
eg. Body thrown with velocity ##v## from surface of earth. Find final height ##h##. (assume ##g## constant)
Method 1: Newton's laws of motion and hence ##v = \sqrt{2gh}##
Method 2: Conservation of energy and hence ##\frac{1}{2}mv^2 = mgh##
So this is an example of what I am looking for.

Conservation of energy is in effect in your method since ##\| v_{in}\| = \| v_{out}\|##

We can't obtain direction by conservation of energy. Right?

 

[HallsofIvy]

You can break the vertical velocity of the ball before the bounce into a component parallel to the inclined plane and vertical to it. Since the plane is at 45 degrees to both horizontal and vertical, that easy. The two components must be equal- calling that equal length "x", we have [itex]x^2+ x^2= 2x^2= v[/itex] so that [itex]x= \frac{v}{\sqrt{2}}[/itex]

 

[RUber]

No matter what method you use, the answer will be the same. You will just be dancing around it differently.
In the problem you are given, using infinite mass for the inclined plane and velocity only for the ball, it lends itself to a collision method to solve.
Any other approach I can think of is unnecessarily complicated.

 

[Faris Shajahan]

Reason I asked this is because I feel like I used to do it another way before. It just bugs me. I can't do anything else basically. It is an issue I have, if I forget something I can't do anything for the next few days!

So if anyone's got any other solution please post it if you don't mind. I don't mind how unnecessarily complicated it is. All you've got to do is hint me to your solution if it terribly long.

TIA