Vectors and Projectiles Legacy Problem #18 Guided Solution

A good problem solver has the habit of reading a problem carefully and constructing a diagram in order to get a mental picture of what's going on. They identify the known and unknown information, they plot out a strategy to get from the givens to the unknown information. Here in this problem I read about an airplane that's currently located south of a border. I'm told that the border is aligned east and west, it's the U.S. Canada border. So what I'm going to do is on my sheet of paper I'm going to draw a horizontal line and below that line, 285 miles south, I'm going to put a dot, and the dot represents the location of the airplane. Now the airplane is located 285 miles south of the border, so I draw a little vertical dash line up to the border, this east-west line that I've drawn, and I label that 285 miles. Now the airplane does not head north to the border, but instead heads a little bit west of north, and so I draw an arrow representing the direction that the airplane's heading. And I label that arrow 189 miles per hour, and it's 20.5 degrees west of the northerly direction, and I label the angle 20.5 degrees in there. What I want to figure out is how much time does it take to get the airplane across the border. So in order to find that information, what I'm going to do is find out how fast the airplane is flying north. After all, I know the northerly direction, the northerly distance to the border, so if I know how fast I'm traveling north, I can find the time that it takes to get north. What I just did there is I plotted out a strategy to get from the givens to the unknown information. Now to execute the strategy, I need my calculator. I'm going to take the 189 miles per hour and multiply it by the cosine of 20.5 degrees. The cosine, because I want to find the northern component, which is the side adjacent 20.5. So I go 189 times the cosine of 20.5, and I get 177.03 blah blah blah miles per hour. That's the northerly speed, the effect of 189 miles per hour in the northerly direction. So now to find the time to go 285 miles north, I'm going to use the equation d equals v times t, one you've known for some time. Rearranging it goes t equals t divided by v, and I take my 285 miles and I divide it by the 177.03 miles per hour. That gives me my answer, my time in units of hours, and if I multiply by 60 minutes per hour, I can get it in units of minutes.