Using relative motion to find direction and time of a boat

[PAstudent]

Homework Statement

A motorboat can move with a velocity of 10.0 m/s, with respect to the water in a river. The river is flowing at 4.00 m/s due east. (a) Calculate the direction (Give the angle with respect to one of the compass directions.) the motorboat must be pointed so that it moves due north with respect to the riverbank? (b) The river is 542 meters wide; calculate the time required for this motorboat to cross the river if it is pointed in the direction calculated in part a.

Homework Equations

Vbg=Vbw+Vwg

The Attempt at a Solution

[/B]

I drew this picture then I found the angle by using arctan(4/10)= 21.8 degrees. My first question is how do you know how to tell the direction it is heading in like west of north or like east of north? Then, I used Pythagorean theorem to find the diagonal vector and it was 10.77 m/s. Does this seem correct so far so that I can find the time?

 

[SteamKing]

If the horizontal vector in your diagram represents the river velocity, I think you drew the diagram backwards.

The usual convention is, due east means the vector points to the right of the page and is horizontal. Due North points to the top of the page and is vertical.

You want the boat to travel due north, which suggests to me that the resultant vector must be vertical.

 

[PAstudent]

I just thought that the vertical vector was the velocity of the boat with respect to the water, the horizontal was velocity of water with respect to ground, and the diagonal was velocity of boat with respect to ground. That's how my teacher did it, but he isn't very clear in his directions