Jon’s Answer to the Garbage Question

Here, below, are Jon’s answers to the questions on yesterday’s post.  If it doesn’t make sense, just read the post below.

Katie was the only one to answer……she gets a copy of this very good book.  Thanks for participating Katie!  It will be going out in tomorrow’s mail.

Well,  As in most of life, there is no right answer.

What is important is how you specify your assumptions and solve the problem based on those assumptions. MY assumptions in writing the question was: Peter is DRIVING. So, he throws the garbage out the window to the left holding the steering wheel with his R hand. I am also assuming he is NOT driving a convertible, so he can’t throw the garbage straight up. I suppose he could have thrown it out to the right, but that would be awkward and would assume the passenger window is open (vis: Harry met Sally), He can obviously not through it “out” backwards.

That would land the garbage in the back seat.

So, Peter, going 40m/hr straight ahead, throws the garbage out straight to the left at 30m/hr. The relative velocity of the garbage would be sqrt(30^2+40^2) or sqrt(900+1600)=50m/hr. So, the garbage travels 50m/hr x2/60 hr = 5/3 m or 1.6m from the point it was thrown out. Now, Peter has traveled 40m/hr x 2/60 hr = 4/3 m or 1.3 miles, The relative DISTANCE of Peter from the garbage would depend on the angle between the two trajectories. ASSUMING a square-angled triangle and that the garbage trajectory would make up the hypotenuse of that triangle, the remaining side would be sqrt(1.6^2 – 1.3^2) or sqrt(25/9m – 16/9 m) = sqrt(9/9 mi^2) = 1 mile.

Part B is the critical one to show you understand the difference of absolute and relative distances/velocities. John stands fixed (in utter disgust at Peter’s lack of environmental responsibility) at the point where the garbage was thrown out, and hence is 1.4 miles away from it when it hits the ground. (we are NOT bothering to figure in the hight from the ground, gravity, 3-dimensional angles, etc). The simplest solution is most often correct. Full credit would be given for a simple diagram that outlines the correct relationships and illustrates an understanding of the concepts even if the numbers are wrong.

Of course, some wise-ass student could simply ASSUME that it was raining and that the windows were closed, so the garbage traveled with Peter all along. THis would violate the problem that states that the garbage did in fact hit the ground.


5 thoughts on “Jon’s Answer to the Garbage Question

  1. You know, I was gonna try to answer, but got hung up on the fact that it took 2 minutes for the trash to hit the ground. That made me think maybe there was a cliff immediately off the left side of the road. A very high cliff. I went off in search of some acceleration formulas and was distracted by something shiney.

  2. I’m with you Scott….I thought two minutes meant it was something like a bag of anti-gravity garbage or something. And also, why didn’t the trash hit the other guy who was walking on the side of the road? In the answer I would have written, the garbage would have knocked him flat, the bag would have exploded and it would have become a community service cleanup project.
    But, since Jon’s knowledge of physics is so far beyond my own, I just assumed there are factors beyond my grasp at work here. Often enough, that is the case.
    What was the shiney thing? Was it Emily’s new car?

  3. No. Emily’s new car is my old car (236,000 miles just can’t be called “new” and certainly not shiney.). My “new” car is a 2007 Honda. I don’t recall what distracted me that day.

  4. I think Scott went in search of the proper way to spell the word “shiny” since that extra “e” got in the way…it was a shiny “e” for sure!

  5. OK, good, now we have Paula and Kristine proofreading for us. I am entirely thankful, and also pretty embarrassed about that.
    If anyone finds any errors in this comment of mine, I will send a copy of that Gene Veith book to them straightaway.

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