2D collision, both angles given, both final velocities unknown.

[joshonator]

I'm trying to figure out what formula to get started in this question:

A 7kg bowling ball moving with a velocity of 8 m/s strikes a single pin of mass 1.36kg. The impact deflects the bowling ball 10 degrees from it's original path. The pin moves along a path 45 degrees from the original path of the ball after the collision. Calculate the velocities of (a) the ball and (b) the pin just after the collision.

Obviously the formula m1v1 + m2v2 = m1v1' + m2v2' can't be used since both final velocities are unknown.

I know that:
P1y = -P2y
Pox = P1x + p2x

Thanks.

 

[Redbelly98]

Welcome to Physics Forums. FYI, I have moved your question to our https://www.physicsforums.com/forumdisplay.php?f=153" area; please post future homework questions there.

I'm trying to figure out what formula to get started in this question:

A 7kg bowling ball moving with a velocity of 8 m/s strikes a single pin of mass 1.36kg. The impact deflects the bowling ball 10 degrees from it's original path. The pin moves along a path 45 degrees from the original path of the ball after the collision. Calculate the velocities of (a) the ball and (b) the pin just after the collision.

Obviously the formula m1v1 + m2v2 = m1v1' + m2v2' can't be used since both final velocities are unknown.

I know that:
P1y = -P2y
Pox = P1x + p2x

Thanks.

The m1v1 + m2v2 = m1v1' + m2v2' formula is really two formulas; one for the x direction and another for the y direction. Try writing the two separate equations, using the angle info, i.e. sin and cos of 10 and 45 degrees.

 

[joshonator]

X: (7)(8) = (7)V1'cos10 + (1.36)V2'cos45
Y: 0 = (7)V1'sin10 - (1.36)V2'sin45

The problem I am having is that there are still two unknowns.

 

[JHamm]

I believe that the angle of the pin should be 35 degrees since the 45 was measured from the deflected ball, which was 10 degrees from your axis. Then you have 2 equations and 2 unknowns

 

[PeterO]

I believe that the angle of the pin should be 35 degrees since the 45 was measured from the deflected ball, which was 10 degrees from your axis. Then you have 2 equations and 2 unknowns

The pin was at 45 degrees to the original path of the ball, not the new direction of the ball!

Perhaps that could have been stated more clearly with the words in a different order.

After the collision, the pin moves along a path 45 degrees from the original path of the ball.

 

[Redbelly98]

I agree that 45 degrees is the correct angle.

JHamm is correct in pointing out that there are now 2 equations for those 2 unknowns, so the unknowns can be solved for.

 

[Zeeshan86]

I am trying to solve the angled 2D-Elastic collision.
I know the final velocity and angle of Mass-2 before and after the collision.
I want to calculate the Velocity and Angle of the Mass-1 before and after the hitting.
Can you help me that how should I proceed ?

 

[Zeeshan86]

What would be the case, if the ball is collided with the plate. Just like the table tennis.
Can we also consider the collision between the table tennis racket and ball as the 2D collision like collision between two ball ? ?
Will the shape of the plate will effect the equations ?