Calculating Relative Velocity of Two Boats in a River

[malawi_glenn]

I have tried calculating with vw=1m/s, but now I see that it can be a little confusing drawing strictly vectors. As I do not know what happens if the speed of the stream is greater than or equal to the relative speed of the boat (In this case, Vw =>1m/s).
View attachment 305287You see... I cannot use the same method, because the drawing is obviosly wrong. The hypothanuse cannot be equal in magnitute, considering speed as a vector quantity...

What is the physical significance of this? :)

 

[Aristarchus_]

What is the physical significance of this? :)

Well, the first thing I thought about was that the boat would never move vertically upwards (in Vy direction) and would just be carried away by the stream, which is intuitively wrong. I have to think about this...

 

[Aristarchus_]

What is the physical significance of this? :)

The boat will first move a little in the vertical direction, after which it would eventually be carried away by the stream. So it will never reach the end of the river...But what distance could it reach? That is, what is the maximum distance it would traverse(in the vertical direction) with the speed of the water greater than its relative velocity?

 

[malawi_glenn]

Well, the first thing I thought about was that the boat would never move vertically upwards (in Vy direction) and would just be carried away by the stream, which is intuitively wrong. I have to think about this...

Why is it intuitively wrong? It make perfect sense. If the water stream speed is greater than the speed which the boat can travel with in the water, the boats can not travel along the line connecting their starting points! If the boats want to travel in a direction perpendicular to the shore, they would have to have a non zero VBx.
This becomes impossible:

 

[Aristarchus_]

Why is it intuitively wrong? It make perfect sense. If the water stream speed is greater than the speed which the boat can travel with in the water, the boats can not travel along the line connecting their starting points!
This becomes impossible
View attachment 305289

Right, but it will move some minimal distance in the y-direction before being carried away, or is this not so?

 

[malawi_glenn]

some minimal distance

zero

 

[Aristarchus_]

zero

Wow, who would've thought... Thank you very much for all the feedback

 

[malawi_glenn]

Wow, who would've thought... Thank you very much for all the feedback

its like dropping a ball at rest. As soon as you release it, it will obtain some velocity > 0 (time is not a discrete variable)

And in the case where VW = 0. The boats can use all their speed in the perpendicular direction and travel along that straight line connecting their original positions using minimal time 10s.

When VW = 1m/s, you can "think of it" as it will take an "infinite" time for the boats to meet at the center of the line connecting their original positions.

You should be able to make a function that give the time needed to meet at centre of that line, with VW as the input