What is the Angle of Deflection in a Colliding Ball and BB Gun Problem?

[mixedmetaphor]

Homework Statement

A 280 g rubber ball is hanging from a 27cm long swing in a booth at a carnival. A little girl shoots it with a BB gun in attempt to win a gigantic, stuffed Daffy Duck doll. The mass of each BB is 3g and the muzzle speed of the gun is 21m/s. If the BB penetrates the ball (and gets stuck inside), what is the mass angle of deflection of the ball?

Homework Equations

p=mv (momentum), conservation of momentum, trigonometry.

The Attempt at a Solution

I feel confident that I could solve this using some trig and momentum if I knew what the problem meant-what is an angle of deflection? If it's what I think it is (at what angle they collide) then could there be one if the two are stuck together? Or is it the angle through which the ball swings? Any ideas?

 

[LowlyPion]

Welcome to PF.

The angle of deflection is the angle the string makes with the vertical.

Solve for the velocity of the combined bullet/ball first. Then use that velocity as the kinetic energy that gets consumed by gravity as it swings upward. KE after impact will of course equal the potential energy PE at its height.

Using that height and an appropriate trig function you should be able to solve directly for the angle.

 

[mixedmetaphor]

Thanks so much, I understand now.