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

In summary, the conversation discusses the use of the equation tan \theta = \frac{vy}{vx} to find the angle at which a ball strikes the ground in a "ball-falls-off-a-cliff" problem. The importance of sketching the path of the ball is also emphasized in understanding the concept.
  • #1
smb360rewind
5
0
Just worked through the "ball-falls-off-a-cliff" problem and was curious as why the equation
[tex]tan \theta = \frac{vy}{vx}[/tex] is used to find the angle at which the ball strikes the ground versus [tex]tan \theta = \frac{sy}{sx}[/tex]

Homework Statement


Homework Equations


The Attempt at a Solution


 
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  • #2
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?
 
  • #3
Thank you. Overlaying the two equations in a sketch reveals your point. I'm starting to understand the importance of "sketching" problems.
 

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

What is the difference between velocity and displacement?

Velocity is a vector quantity that describes the rate of change of an object's position in a specific direction, while displacement is a vector quantity that describes the change in an object's position from its initial position to its final position.

How are velocity and displacement related?

Velocity and displacement are related by the equation v = Δx/Δt, where v is velocity, Δx is displacement, and Δt is the change in time. This means that velocity is the change in displacement over a given time interval.

What is the unit of measurement for velocity and displacement?

The SI unit for both velocity and displacement is meters per second (m/s). This can also be expressed as meters per hour (m/h) or kilometers per hour (km/h).

Can an object have a non-zero velocity but a zero displacement?

Yes, an object can have a non-zero velocity but a zero displacement. This can happen when the object moves in a circular path, where the displacement is always zero but the velocity is constantly changing.

How does the slope of a distance-time graph relate to velocity?

The slope of a distance-time graph represents the velocity of an object. A steeper slope indicates a higher velocity, while a flatter slope indicates a lower velocity. A horizontal line on a distance-time graph represents an object with a constant velocity of zero.

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