Sailboat's Velocity
A sailboat has coordinate (x1,y1) at time t1. two minutes later, at time t2, it has coordinates (x2,y2). What it the average velocity of the boat?
I can find the magnitude by averaging the two components. How do I find the direction?
Answer
Based on your wording regarding the magnitude, I am suspicious that you may have made a mistake in calculations. When working in multiple dimensions, you're going to have to be careful about how you get the magnitude.You have to treat each direction (x and y) separately and finding the total is not a simple average. Once you obtain the average velocity for each direction, the magnitude is obtained by
v = sqrt[(v_x)^2+(v_y)^2]
rather than averaging them. Essentially, you have to treat each component like a leg of a right triangle with the total as the hypotenuse.
Similarly, when it is time to get the direction you would calculate it like calculating the angle of a right triangle. Treat v_x as the adjacent side, v_y as the opposite side, and the magnitude v as the hypotenuse. Since you have all three of those you can pick your favorite trigonometric function to find the angle.
Customer support service by UserEcho
Based on your wording regarding the magnitude, I am suspicious that you may have made a mistake in calculations. When working in multiple dimensions, you're going to have to be careful about how you get the magnitude.You have to treat each direction (x and y) separately and finding the total is not a simple average. Once you obtain the average velocity for each direction, the magnitude is obtained by
v = sqrt[(v_x)^2+(v_y)^2]
rather than averaging them. Essentially, you have to treat each component like a leg of a right triangle with the total as the hypotenuse.
Similarly, when it is time to get the direction you would calculate it like calculating the angle of a right triangle. Treat v_x as the adjacent side, v_y as the opposite side, and the magnitude v as the hypotenuse. Since you have all three of those you can pick your favorite trigonometric function to find the angle.