The Nazi Party: Background & Overview

Since that diagonal line is 1 m/s, the horizontal and vertical lines should be .7 m/s. You should get about .7 the length of the diagonal line. Figure 2-3: Vectors are equal to each other if they have the same length and distance, they are not equal to each other if they are of different lengths ("magnitudes") even if they’re in the same direction, nor are they equal to each other if they have the same magnitude but different directions. Vectors are considered equal if they have the same length (mathematicians call this the "magnitude" of the vector) and the same direction. It’s customary to write vectors in bold face (or if on a blackboard, by drawing a line with a little arrowhead over the letter). Hitler and other Nazi leaders travelled round the country giving speeches putting over this point of view. Hitler was furious and threatened to shoot them and then commit suicide: "I have three bullets for you, gentlemen, and one for me! You have to add the mass times velocity, before and after, and that will be conserved.

The total distance is equal to the elapsed time, t, times the speed or velocity (depending on whether you want just the distance, or the distance and direction). So if you do some experimenting, it seems like what might be getting conserved is not velocity, but something that is the product of mass times velocity. If you think back to last time, I talked about force, mass and acceleration. For that matter, if you think about it, the mass of the rocket was declining while we did that first burn, so we must have gained a tiny bit more than 4 m/s even the first time around. That’s quite true, actually, and the real formula for how much velocity a rocket gains by burning some amount of fuel is a bit more complex. For example the beaks of garfish don't give much of a hook hold and the small mouths of wrasse can't easily absorb a big hook. He would hold the post for the remainder of his life. But if it’s a conservation law, it has to hold all of the time, not just in billiards scenarios. This is actually just another way of stating the conservation of momentum.

That way we can avoid the use of a fudge factor, since the units are already consistent with each other. Some species are just particularly difficult to hook. As soon as the masses are different the tidy behavior we illustrated above goes right out the window and the player can’t predict what will happen. A pool player will have played so many games of pool that he knows this behavior in his gut; he knows exactly where to hit the other ball with the cue ball to get the angle he wants, to send that other ball into the corner pocket. A billiard ball moves when struck with a cue. And, since I did contrive this scenario, the direction of the cue ball is 30 degrees "up" from the x axis, and its speed is 0.866 m/s. Reverse the process, hitting the cannonball with the cue ball, and it will barely budge, but the cue ball will bounce back the way it came. Hit a pool ball with a cannonball and the pool ball will go rocketing away, much faster than the cannonball was moving, and the cannon ball will slow down the tiniest but not stop moving. That doesn’t look very much like velocity was conserved, does it?

What you do on a diagram, is make the arrow that much longer or shorter. On a diagram, take your first vector, whatever it is, and then put your second vector so that its tail is right at the head of the first vector. Then draw a new vector from the tail of the first vector to the head of the second vector. For convenience when they draw diagrams, the x direction is to the right, and the y direction is upward, the y axis being 90 degrees counterclockwise from the x axis. There’s no notion built into a vector of "where it starts" and "where it ends." We can move them around for convenience, especially on those diagrams, just so long as we don’t stretch them or rotate them. So now let’s go back to the pool table, make the scenario slightly more complicated and see what we can use this whiz-bang vector thing to figure out. DIAMETER. PICTURES A GAME TABLE, 3 BILLIARD BALLS, WITH "BILLIARD RUSSE" OR RUSSIAN BILLIARDS. And it would go right off the pool table, too, if not for the bumpers.

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