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An important concert in the study of physics, and in particular, the study of mechanics, is the concept that there is no absolute frame of reference. What this means can be expressed in two ways.
First, when any two observers measure the motion of an object, what they measure is determined by the observer. For example, watch the video of the swan below. |
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The swan appears to be stationary when the camera is stationary. If the camera is moving, this one can either appear moving forward or moving backward, depending on what the camera is doing. All are correct as they depend on what the camera sees. What we therefore say is that the motion of the swan is relative to the camera in this case.
Another way we can express this is that there is no absolute frame of reference, or what we determined to be the true absolute origin - the coordinates being (0, 0) in a 2 dimensional space, or (0, 0, 0) in a three dimensional space.
These coordinates are the origin origin for the OBSERVER, with each observer determining what they see as their origin
Another way we can express this is that there is no absolute frame of reference, or what we determined to be the true absolute origin - the coordinates being (0, 0) in a 2 dimensional space, or (0, 0, 0) in a three dimensional space.
These coordinates are the origin origin for the OBSERVER, with each observer determining what they see as their origin
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Theory
Watch the video, which look at the concepts rectilinearly and then in two dimensions. It is advised you have watch the video on vectors beforehand. |
Sample Problem
We are now ready to try a sample problem
Below is a sample problem with a video that explain how to solve it. It is suggested you try the problem beforehand, as this actually aids understanding, even if you are unsure if you are correct.
We are now ready to try a sample problem
Below is a sample problem with a video that explain how to solve it. It is suggested you try the problem beforehand, as this actually aids understanding, even if you are unsure if you are correct.
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Interactive
Let's apply what you've learnt.
The following interactive (courtesy Tom Wash) allows you to set the river velocity and the velocity of the boat relative to the river. It then determines the velocity of the boat relative to the Earth.
Are useful way to use is to set the variables and then calculate the velocity of the boat, using the animation to check your answer.
Let's apply what you've learnt.
The following interactive (courtesy Tom Wash) allows you to set the river velocity and the velocity of the boat relative to the river. It then determines the velocity of the boat relative to the Earth.
Are useful way to use is to set the variables and then calculate the velocity of the boat, using the animation to check your answer.
More problems to try
- An aeroplane has a velocity of 240 km/h north according to its instruments. A cross wind of 100 km/h is blowing from the west. Where will the aircraft be after two hours?
(520km , N23°E) - A boat travels at 10 m/s North relative to the water in a river where the current is 10 m/s west. Find the velocity of the boat relative to the river bank. (14m/s , NW)
- A sailor stands on the deck of the ship which is travelling at 20 km/h north. He looks up and sees an albatross flying at 28 km southeast relative to the ship. What is the velocity of the albatross relative to the ocean floor? (20km/h E)
- Three swimmers can swim equally fast related to the water. They have a race to see who can swim across the river in the least time. Swimmer A swim is perpendicular to the current and lands on the far side shore downstream because the current has swept him in that direction. Swimmer B swims upstream at an angle to the current and lands on the far shore directly opposite the starting point. Swimming C swims downstream at an angle to the current in an attempt to take advantage of the current. Who crosses the river in the least time? Account for your answer.
