For my homework, I was given a set of river problems relating to vectors. What I am really struggling with is creating a diagram out of the given information as I always fail to make an accurate representation of the provided information.
As for an example, here is a question which I do not quite understand.
Mary leaves a dock, paddling her canoe at 3 m/s. She heads downstream at an angle of $30^\circ$ to the current, which is flowing with 4 m/s.
- How far downstream does Mary travel in 10s?
- What is the length of time required to cross the river if its width is 150m?
So, what I have tried to do is:
Since I know that the triangle is a right-angled (Would be greatly appreciated to know of a way to determine whether each triangle is right-angled or not since I only based this assumption on my diagram which again, in my opinion, isn't accurate.) I have tried plotting a diagram to visualize the question (You can see it here), and solving for side d using sin. However, I got that d = 3sin30, which when I tried finding the time using the formula d = vt, I got the wrong answer according to my textbook.
I really am lost, and I don't completely understand where I messed up. Could someone perhaps explain to me what I have done wrong? I am almost sure that I didn't draw the diagram correctly as I feel that the problem is with my understanding of the question.
Thanks a whole bunch!
There are several assumptions/ misconceptions, you almost found. First one, there is no need for right angle. In fact, in your figure, for a right angle triangle the hypotenuse ($3$) must be greater than any of the sides (you have one with length $4$). So let's start from your figure, but you need to keep only the line denoting the motion of the canoe, at $30^\circ$ with respect to the current. If there would be no current, in one second the canoe will travel $3\sin 30^\circ$ meters in the direction across, and $3\cos 30^\circ$ down the river. If you add the current, it has no component in the perpendicular direction, so you still move $3\sin 30^\circ$, but in the downstream direction the canoe is traveling $3\cos 30^\circ+4$ meters. To draw the diagram, start with the speed of the canoe vector, as you have done in your figure, then from the end of that vector draw a vector of length $4$ in the downstream direction. To obtain the velocity with respect to the starting point just join the starting point with the end of the vector representing the current velocity.