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

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AI Thread Summary
The problem involves a rubber ball being shot by a BB gun, with the goal of determining the angle of deflection after the BB becomes embedded in the ball. The angle of deflection refers to the angle the swing makes with the vertical after the collision. To solve this, one must first calculate the velocity of the combined mass of the ball and BB using conservation of momentum. This velocity is then converted into potential energy as the ball swings upward, allowing for the calculation of the height reached. Finally, trigonometric functions can be applied to find the angle of deflection based on the height achieved.
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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.
 
Last edited:
Thanks so much, I understand now.
 

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