Vectors and Projectiles Legacy Problem #17 Guided Solution

As I started in on the solution of the problem, there was something that I naturally did. I picked up a pen, got myself a sheet of paper and some space to write, and I started diagramming the situation in an effort to take this verbal description and transform it into a picture that I could relate to. And that's a habit of an effective problem solver. I, on my diagram, I drew a picture of town. I put a dot on the sheet of paper. I labeled it down. And then as I read, I noticed there's a tornado, so I had to find the location of the tornado. So I traced a line 12 kilometers south, just a vertical line south of my town dot, and I labeled it 12. And then I traced a little line horizontally from that point towards the west. And where that ended, I put a dot, and I labeled that dot as tornado. And I've labeled this 12 kilometers south and this 23 kilometers west. And then I drew a vector that went from the tornado to my town, and I labeled that vector a resultant, or r. And what I wish to do in the first part of the problem is find out how far is that dot tornado from that dot labeled town. And I recognize that all I have to do is use the Pythagorean theorem and find the hypotenuse of a triangle that has as its sides 12 kilometers south and 23 kilometers west. So I did 12 squared plus 23 squared to get the hypotenuse, and that came out to be 25.9422 blah blah blah blah blah. And that is the distance that that tornado is from that town. Now, once you've done that, take a deep breath, and now all you have to do is use a very simple equation you've likely known for some time, that the distance equals the velocity times the time, or the speed times the time, or the rate times the time, d equals vt. And what you want to do is solve that equation for t. So you could rearrange it to say t equals d divided by v. And now take your d, you've just calculated this 25.9422, and then put in the numerator and put the 82 kilometers per hour in the denominator. Now the kilometers cancel and you end up getting hours as the time. 0.316 hours is the time, and to convert that to minutes you just simply multiply by 60. And that's the mathematics of determining the approximate time it takes for a tornado to get from one location to another location.