Finding the magnitude and direction of a boat's motion

[Abdullah Younas]

Homework Statement

A boat is traveling upstream in the positive direction of an x
axis at 14 km/h with respect to the water of a river. The water is
flowing at 9.0 km/h with respect to the ground.What are the (a)
magnitude and (b) direction of the boat’s velocity with respect to
the ground?

Relevant Equations

For direction : θ=tan^(-1)⁡〖Y/X〗
For Magnitude: √(A^2+B^2 )

Homework Statement: A boat is traveling upstream in the positive direction of an x
axis at 14 km/h with respect to the water of a river. The water is
flowing at 9.0 km/h with respect to the ground.What are the (a)
magnitude and (b) direction of the boat’s velocity with respect to
the ground?
Homework Equations: For direction : θ=tan^(-1)⁡〖Y/X〗
For Magnitude: √(A^2+B^2 )

The formula for magnitude is √(A*A)+(B*B) but simply subtracting the magnitude of speeds and the farmula of direction is θ=tan INVERSE(Y/X).
but simply shows the direction into +ve and -ve x-axis. what is the best solution of the problem?

 

[haruspex]

but simply shows the direction into +ve and -ve x-axis.

Please explain what you mean by that.

Why are the "relevant equations" you quote relevant to this problem? I.e. what do the A and B or X and Y in them correspond to in the question?

 

[travellinglee]

Am I missing something? From the information in the question the only thing that can be calculated is the speed. I'm willing to be educated but I can't see how the magnitude/mass can be calculated from the info provided and neither can direction (assuming direction is expected as degrees, minutes and seconds). I think I'm in at the deep end here.

 

[haruspex]

magnitude/mass

Mass?? There is no mention of mass in the question. It asks for the magnitude of the velocity, i.e. the speed.
Do you understand what is meant by the magnitude and direction of a vector?

assuming direction is expected as degrees, minutes and seconds

In general, yes you can figure out, in degrees, the direction of the velocity wrt the ground, given the velocity of the river and the velocity of the boat relative to it.
In the present case, it is almost trivial because the two given velocities are parallel to the same axis (termed here the x axis). So in this case it is simply a matter of deciding whether the boat is going upstream or downstream.

 

[travellinglee]

I obviously don't understand the term 'magnitude' in terms of physics terminology, in my uneducated world 'magnitude' is a general reference to the size and/or weight of an object, please explain. As far as direction in concerned I was expecting the answer to be more than just 'upstream' or 'along the X axis', something more like 0°, 0', 0'' e.g. North. Sorry for asking all these questions, it's a learning curve.

 

[Abdullah Younas]

Please explain what you mean by that.

Why are the "relevant equations" you quote relevant to this problem? I.e. what do the A and B or X and Y in them correspond to in the question?

I am supposing A or B and X or Y values .

 

[haruspex]

I am supposing A or B and X or Y values .

That's not what I asked.
You have a boat and a river, both moving. How do those directions of movement relate to X and Y in your equations?
You may need to read the question more carefully. It says: "A boat is traveling upstream".

 

[haruspex]

I obviously don't understand the term 'magnitude' in terms of physics terminology, in my uneducated world 'magnitude' is a general reference to the size and/or weight of an object, please explain. As far as direction in concerned I was expecting the answer to be more than just 'upstream' or 'along the X axis', something more like 0°, 0', 0'' e.g. North. Sorry for asking all these questions, it's a learning curve.

For magnitude, see https://en.m.wikipedia.org/wiki/Euclidean_vector.
For direction, it doesn't have to be a compass direction. In this question we are given the direction of the boat relative to the river as upstream. What we are asked to find out is whether it is upstream or downstream relative to the bank.