Relative Velocity: Difference between revisions
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Claimed by Lily Masters (Fall 2016) | Claimed by Lily Masters (Fall 2016) | ||
The motion of an object may look different when viewed from a different reference frame. This can be described by defining the relative velocity of the reference frame. | |||
==Relative Velocity== | |||
When an object is moving in a medium that is also moving, its velocity may be different depending on the location of the observer. For example, consider a boat moving through a flowing river. If the observer is aboard the boat, the velocity will be different than if the observer was standing by the side of the river. This can be more easily described through vector addition with one reference frame considered an intermediate reference frame: | |||
<math>\vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC}</math> | |||
This means that the velocity of A with respect to C is equal to the sum of the velocity of A with respect to B and the velocity of B with respect to C. In this case, B is the intermediate reference frame. | |||
==Examples== | |||
===Airplane in Wind=== | |||
An airplane is flying with a velocity of <math>\vec{v}_{PA}</math> relative to the air. The wind is moving with a velocity of <math>\vec{v}_{AG}</math> relative to an observer on the ground. The velocity of the plane relative to the ground can be found using vector addition: | |||
<math>\vec{v}_{PG} = \vec{v}_{PA} + \vec{v}_{AG}</math> | |||
Suppose the plane is moving with a velocity of <math>\left \langle {150,20,0} \right \rangle</math> km/h relative to the air. The wind is moving with a velocity of <math>\left \langle {-25,0,-10} \right \rangle</math> km/h relative to the ground. What is the velocity of the plane relative to the ground? | |||
Answer: | |||
<math>\vec{v}_{PG} = \left \langle {150,20,0} \right \rangle + \left \langle {-25,0,-10} \right \rangle</math> | |||
<math>\vec{v}_{PG} = \left \langle {125,20,-10} \right \rangle</math> | |||
==Connectedness== | |||
#How is this topic connected to something that you are interested in? | |||
#How is it connected to your major? | |||
#Is there an interesting industrial application? | |||
== See also == | |||
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context? | |||
===External links=== | |||
Internet resources on this topic | |||
==References== | |||
This section contains the the references you used while writing this page | |||
[[Category:Interactions]] | |||
Revision as of 16:39, 27 November 2016
Claimed by Lily Masters (Fall 2016)
The motion of an object may look different when viewed from a different reference frame. This can be described by defining the relative velocity of the reference frame.
Relative Velocity
When an object is moving in a medium that is also moving, its velocity may be different depending on the location of the observer. For example, consider a boat moving through a flowing river. If the observer is aboard the boat, the velocity will be different than if the observer was standing by the side of the river. This can be more easily described through vector addition with one reference frame considered an intermediate reference frame:
[math]\displaystyle{ \vec{v}_{AC} = \vec{v}_{AB} + \vec{v}_{BC} }[/math]
This means that the velocity of A with respect to C is equal to the sum of the velocity of A with respect to B and the velocity of B with respect to C. In this case, B is the intermediate reference frame.
Examples
Airplane in Wind
An airplane is flying with a velocity of [math]\displaystyle{ \vec{v}_{PA} }[/math] relative to the air. The wind is moving with a velocity of [math]\displaystyle{ \vec{v}_{AG} }[/math] relative to an observer on the ground. The velocity of the plane relative to the ground can be found using vector addition:
[math]\displaystyle{ \vec{v}_{PG} = \vec{v}_{PA} + \vec{v}_{AG} }[/math]
Suppose the plane is moving with a velocity of [math]\displaystyle{ \left \langle {150,20,0} \right \rangle }[/math] km/h relative to the air. The wind is moving with a velocity of [math]\displaystyle{ \left \langle {-25,0,-10} \right \rangle }[/math] km/h relative to the ground. What is the velocity of the plane relative to the ground?
Answer:
[math]\displaystyle{ \vec{v}_{PG} = \left \langle {150,20,0} \right \rangle + \left \langle {-25,0,-10} \right \rangle }[/math]
[math]\displaystyle{ \vec{v}_{PG} = \left \langle {125,20,-10} \right \rangle }[/math]
Connectedness
- How is this topic connected to something that you are interested in?
- How is it connected to your major?
- Is there an interesting industrial application?
See also
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?
External links
Internet resources on this topic
References
This section contains the the references you used while writing this page