Homework Help: Collision response of two object

Hi,
how can i find collision response between rectangle and circle like in this picture :



i want to identify the direction and magnitude of V1 vector and the V2 vector after they collided , does anyone have some idea about this ?

 

Okey, in this picture :


With :
+ V1 : initial velocity vector of Circle
+ M1 : mass of Circle
+ V2 : initial velocity vector of Rectangle
+ M2 : mass of Rectangle

i want to identify the direction and magnitude of V1 vector and the V2 vector after they collided, does anyone have some idea about this ?

 

Please look at this picture :



First, we consider that :

+ v1i : veloc vector of circle BEFORE they collide
+ v2i : veloc vector of rectangle BEFORE they collide
+ v1f : veloc vector of circle AFTER they collide
+ v2f : veloc vector of rectangle AFTER they collide​

How to find V1f and V2f

*Before the collision
+Momentum of the objects:

p1i = m1*v1i
p2i = m2*v2i
Pi = p1i+p2i​

+Kinetic energy of the objects:

ke1i = (1/2)*m1*v1i2
ke2i = (1/2)*m2*v2i2
KEi = ke1i+ke2i​

*After the collision

p1f = m1*v1f
p2f = m2*v2f
Pf = p1f+p2f​

+Kinetic energy of the objects:

ke1f = (1/2)*m1*v1f2
ke2f = (1/2)*m2*v2f2
KEf = ke1f+ke2f​

*Apply the law of the conservation of momentum

Pi = Pf = P
m1*v1i+m2*v2i = m1*v1f+m2*v2f
KEi = Kef
(1/2)*m1*v1i2+(1/2)*m2*v2i2 = (1/2)*m1*v1f2+(1/2)*m2*v2f2​

*Rearranging and combining the two equations above, we get the following:

v1i-v2i = v2f-v1f
V = v1i-v2i
So,
v1f = v2f-V ​

*Using the above equation with the equation for P, we get the final results:

v2f = (P+V*m1)/(m1+m2)
v1f = v2f-v1i+v2i
​

So we know the way how to find V1f and V2f,and we have this :

V1i = V1;
V2i = V2;​

And m1,m2, so we can find v1f,v2f
But seem they have something wrong but i don’t know,
Uhm,Hope u can tell me. Thanks alot.