What Conditions Allow a Thrown Ball to Return to the Thrower?

[pinsky]

Hello!

Can someone help me define the necessary condition in which the ball returns back to the thrower?

a,b and c are angles.

The changeable value can be either a,b or V0, irrelevant.

I don't know if there is a condition concerning the angle b, should it be 90°?

In that case if a=0 the ball would just continue jumping at the spot where it hits the ground.

(the dotted line should represent the parabolic flight, haven't figured out jet how to draw that nicely :) )

 

[tiny-tim]

hello pinsky!

the ball doesn't have to follow the same path to return to the thrower

anyway, what is the coefficient of restitution (the amount of energy lost ono the bounce)? or is it completely elastic?

 

[pinsky]

Hello tim

The ball is completely elastic.
I now see that i forgot to mention, I'm looking for the condition in which the ball returns in one bounce.

(lets say that a and v0 are constants)
I suppose one could also define a relation between the number of bounces and the angle b , me not being the one :) .

 

[tiny-tim]

ok, then a 90° angle should return the ball over the same path

but there may be another solution …

there are usually two angles for which a given speed will have a given range, so i suppose it could bounce in at one angle and out at the other (but i haven't done the maths to check it)