I'm doing a set of homework questions but I can't figure out how to do this one:
An oceanliner is heading due north with a speed of 8.5 m/s relative to the water. A small sailboat is heading 45° east of north with a speed of 1.0 m/s relative to the water. Find the relative velocity (magnitude and direction) of the sailboat as observed by the passengers on the ocean liner. Determine the directional angle relative to due north.
What I know (o=oceanliner, s=sailboat, w=water):
Vow=8.5m/s due north
Vsw=1.0m/s 45 degrees east of north
So Vso=Vow + Vws, which means Vso is 7.5m/s? Or is that only true for when both objects are going the same direction? And then how would I find the angle?
I'm just really confused..
An oceanliner is heading due north with a speed of 8.5 m/s relative to the water. A small sailboat is heading 45° east of north with a speed of 1.0 m/s relative to the water. Find the relative velocity (magnitude and direction) of the sailboat as observed by the passengers on the ocean liner. Determine the directional angle relative to due north.
What I know (o=oceanliner, s=sailboat, w=water):
Vow=8.5m/s due north
Vsw=1.0m/s 45 degrees east of north
So Vso=Vow + Vws, which means Vso is 7.5m/s? Or is that only true for when both objects are going the same direction? And then how would I find the angle?
I'm just really confused..
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V A relative to B is also V A relative to X - V B relative to X
So in your terminology
Vos = Vow - Vsw = Vow + ( -Vsw )
Now as these are vectors you can draw them on paper to see what happens.
Draw an arrow 8.5 cm up the page with the head at the top ( north)
Now from the tip of this draw the vector of ( -Vsw) which will have a length of 1cm and it will be down the page and to the left. i.e the opposite direction to E of N.
The tip of this arrow will be pointing downwards.
These two together form the expression Vow + (- Vsw)
The resultant or equivalent vector starts from the beginning of the first and its arrow is at the end of the second vector.
Hence it is up the page ( sort of North) angled to the left ( about 15 degrees west of north by just picturing it in my mind) and somewhat shorter than the first vector ( about 7.8 m/s roughly)
To do it by algebra you must resolve each vector into its components of North and West, Only add components that are inthe same direction.
And you are left with two components. One North and one West.
Use Pythagoras' theorem to calculate the magnitude of the result, and find theta from your tangent rule. tan(theta) = opposite/ adjacent.
If you need to, revise your trigonometry. But please, DO draw the triangle first.
It will help you to understand vectors better.
So in your terminology
Vos = Vow - Vsw = Vow + ( -Vsw )
Now as these are vectors you can draw them on paper to see what happens.
Draw an arrow 8.5 cm up the page with the head at the top ( north)
Now from the tip of this draw the vector of ( -Vsw) which will have a length of 1cm and it will be down the page and to the left. i.e the opposite direction to E of N.
The tip of this arrow will be pointing downwards.
These two together form the expression Vow + (- Vsw)
The resultant or equivalent vector starts from the beginning of the first and its arrow is at the end of the second vector.
Hence it is up the page ( sort of North) angled to the left ( about 15 degrees west of north by just picturing it in my mind) and somewhat shorter than the first vector ( about 7.8 m/s roughly)
To do it by algebra you must resolve each vector into its components of North and West, Only add components that are inthe same direction.
And you are left with two components. One North and one West.
Use Pythagoras' theorem to calculate the magnitude of the result, and find theta from your tangent rule. tan(theta) = opposite/ adjacent.
If you need to, revise your trigonometry. But please, DO draw the triangle first.
It will help you to understand vectors better.
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make a vector diagram with the water as th ezero of XY
solve the problem then make a coordinate centered on the boat with zero velocity and "tilted XY " with respect to the water xy
stare at it until the "light bulb " in your head goes on
it is called transformation of coordinate systems
the idea was critical to Einstein for relativity
these kinds of navigational problems were vital for ships captains and navigators
submarines used the idea for torpedo attacks. they had to shoot for where the boat would be and the boat had to "zig zag" so they could escape
solve the problem then make a coordinate centered on the boat with zero velocity and "tilted XY " with respect to the water xy
stare at it until the "light bulb " in your head goes on
it is called transformation of coordinate systems
the idea was critical to Einstein for relativity
these kinds of navigational problems were vital for ships captains and navigators
submarines used the idea for torpedo attacks. they had to shoot for where the boat would be and the boat had to "zig zag" so they could escape