# Energy and Momentum conservation, what else?

Note: there is no friction at all.

General problem: A ball moves (in speed v1) toward a quarter of a circle (which was stand still before the ball touched it and can move on x) and walks on it until it leaves it. How may I find the balls speed on x and y?

I have attached the following image to make the problem easier:

In this kind of questions, we use save of energy and save of linear momentum on x.

Using save of energy gives me the value of the ball's speed But How may I get the speed on x direction and y direction of the ball?

Using save of momentum gives me an expression with two variables, the ball's speed on x and the mass's speed on x. (Which doesn't help since I don't know both of them)

Am I missing something here?

• Any idea please? I am not thinking of another method for this? It sounds like I'm missing something
– dan
Nov 1, 2020 at 16:36
• (1) if this is homework then please add the homework tag. (2) I suggest you first decide if the ball flies off the top, or does it come back down? If it comes back down then think about the overall effect. Nov 1, 2020 at 19:16
• I don't know if you've learnt D'Alambert virtual work method. I guess the problem is easier using it. Nov 1, 2020 at 21:29
• @AndrewSteane What do you mean by fly or come back? sure it will come back to the ground since mg affects the ball. How this is going to help me?
– dan
Nov 1, 2020 at 23:12
• I mean there are two cases: at low speed the ball rises a little way up the slope then rolls back down. At high speed it flies off the top and you have to decide what it will do after that. Nov 2, 2020 at 8:42

When the ball exits from the top, the ball's speed in $$x$$ and the ramps speed are the same. Because just before exiting, the ball was in contact with the ramp. If it was slower, the ball wouldn't be in contact, whereas if it was faster, the ramp would deform. This will eliminate one variable and permit you to solve the two equations.