How do I calculate the deflection angle in a bowling split conversion?

[Return]

[SOLVED] Deflection Angle

Hey guys, back again lol, got a really quick question:

In order to convert a tough split in bowling it is necessary to strike the pin a glancing blow as shown. Assume that the bowling ball, initially traveling at 12.0 [m/s], has five times the mass of the pin and that the pin goes off at 80[degrees] from the original direction of the ball. Calculate the speed A) of the pin and B) of the ball just after collision and C) calculate the angle through which the ball as deflected. Assume the collision is elastic and ignore any spin of the ball.


So far I've done part A and part B, but I'm ashamed to say I'm having trouble calculating the angle. Do I make a resultant triangle? A point in the right direction would be great

^ ^ thank you!

Return

 

[tiny-tim]

Hi Return!

You know all three speeds, and one angle, whic is more than enough information … you can use conservation of momentum in the original direction of the ball, or perpendicular to it, or you can draw a resultant triangle.

 

[Return]

So if I want to use the velocities, I use the law of cosines right?

 

[tiny-tim]

law of cosines?

if you mean that the component of a vector (like a velocity or a force) in a particular direction is the value of the vector times the cosine …
… then yes! ​