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

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SUMMARY

The discussion centers on calculating the angle of deflection for a rubber ball struck by a BB in a carnival game scenario. The rubber ball has a mass of 280 g and is suspended from a 27 cm long swing, while the BB has a mass of 3 g and a muzzle speed of 21 m/s. The angle of deflection refers to the angle the swing makes with the vertical after the collision. To find this angle, one must first calculate the combined velocity of the ball and BB post-collision using the conservation of momentum, and then apply trigonometric functions to determine the height reached and the corresponding angle.

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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?
 
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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.
 
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Thanks so much, I understand now.
 

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