What is the relationship between velocity and displacement in a falling object?

AI Thread Summary
The discussion explores the relationship between velocity and displacement for a falling object, specifically in the context of a ball falling off a cliff. It highlights the use of the equation tan θ = vy/vx to determine the angle of impact, contrasting it with tan θ = sy/sx. The trajectory of the ball is identified as parabolic, emphasizing that the velocity vector at impact does not align with the slope of the line connecting the cliff to the impact point. The importance of sketching the problem to visualize these concepts is also noted. Understanding these relationships is crucial for solving projectile motion problems effectively.
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Just worked through the "ball-falls-off-a-cliff" problem and was curious as why the equation
tan \theta = \frac{vy}{vx} is used to find the angle at which the ball strikes the ground versus tan \theta = \frac{sy}{sx}

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Draw a sketch of the path of the ball from the cliff to the ground. The trajectory is a curve (parabolic). The "direction that the ball strikes the ground" is the direction of the velocity vector just before impact. Can you see that the velocity vector at impact does not have the same slope as the straight line drawn from the point where the ball leaves the cliff to the point of impact?
 
Thank you. Overlaying the two equations in a sketch reveals your point. I'm starting to understand the importance of "sketching" problems.
 
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