... displacement by component method. I hope anyone will seriously take this cause I badly need it, and might as well give the full detailed answer with its equation so that I can study it for my prelims.
Answers (1)
Get a paper and draw an arrow labeled "N" and an arrow labelled "E". A line going NE will cast a shadow on the "N" line which is the tangent of 45 degrees, and a shadow on the "E" line which is the cotangent of 45 degrees. The tangent is 0.707 so the shadow, actually called the projection, is 250 x 0.707 = 176.75 miles North. The cotangent is also 0.707 so the East projection is 250 x 0.707 = 176.75 miles East.
Now if you go 150 miles west from there the resultant is 26.75 miles East and 176.75 miles North. It's easy to get confused with this, but it helps a lot to draw the lines. You can see that a line from the start to the resultant is an angle greater than 45 degrees. So when you figure the tangent of that angle to be 26.75 divided by 176.75, the answer is 8.6 degrees and that is wrong. So you figure 176.75 divided by 26.75 and you get 81.4 degrees. The length of the resultant is found by the Pythagorean Theorem: The square of the hypotenuse equals the sum of the squares of the other two sides. 176.75 squared is 31240.5625 and 26.75 squared is 715.5625 and the sum is 31956.125 and the root of that is 178.76 miles.
ANSWER: 178.76 miles at 81.4 degrees East.