How High Will the Ball Bounce on an Inclined Plane?

AI Thread Summary
The discussion focuses on the behavior of a ball bouncing on an inclined plane, specifically analyzing the vertical speed after impact and the relationship between angles during elastic collisions. The vertical speed is calculated using the formula v_y = √(2gh) cos(2α), prompting inquiries about the mathematical reasoning behind the cosine factor. Participants explore the principles of vector components and the fundamental law that the angle of incidence equals the angle of reflection. A diagram illustrating the initial and final velocity vectors is suggested to clarify these concepts. Understanding these dynamics is crucial for predicting the ball's height and trajectory post-impact.
Faefnir
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A ball, which can be regarded as pointin all its effects, falls steady , subject only to the weight force, on an inclined plane of an angle α with respect to the horizontal from a height h computed from the impact point. The ball bounces elastically. Get the d height can reach the ball and the falling parabola characteristics after the impactAfter impact vertical speed:

$$ v_{y} = \sqrt{2gh} \cos (2 \alpha) $$Why ## \cos (2 \alpha) ##? There is a mathematical explanation for this? Yes, I know about vectorial speed components, but why exactly this corner?
 
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What's the relationship between the angle of incidence and the angle of reflection when something bounces elastically off of a surface?
 
angle of incidence = the angle of reflection
 
Faefnir said:
angle of incidence = the angle of reflection
Right! So draw yourself a diagram of the initial and final (pre and post collision) velocity vectors, showing the angle between them. Then find the vertical component of that final velocity.
 
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