2007-09-07

Today's nonsense
- Math club Monday morning will be bagging stuff to sell
- WD40? Use it to clean your shower doors, there's nothing harmful about it. Or use it as a lubicrant for hinges. Apparently it's a product that displaces water, it's antirust, and on their 40th attempt, they came up with this formula, so WD40 - Water Displacement 40. You've got to see the uses. Anyway.
- Katie being charged $6.66
- Megan's change of $5.55
- Phoebe and the movie "The Number 23" and being freaked out by her jacket with the number 23 on it.
- Dropping a monkey from the air from a magnet when a dart-shooter is shot at it .. some sort of wiring system to set it all up?

You do not have to do #64. We will get through some homework problems and then give Dakota that phone call that he needs so much.

Still working on that #71 bus problem

We are starting with the same #71 as from yesterday. A bus accelerates 1.5 m/s^2 from rest for 12 seconds, and then goes at constant speed for 25 seconds, and then slows to a stop with an acceleration of -1.5 m/s^2. What was the displacement (distance) traveled?

The total distance is distance 1 + distance 2 + distance 3 because the problem is broken into three parts. So the first distance is acceleration = (change in v)/(change in t), so the change in v is going to be a * (change in t). And we know that the change in time is 12 seconds and that it accelerates at 1.5 m/s^2. So that's 1.5 * 12, and that's our change in velocity. Since it started from 0 the final velocity is 18, and the average velocity over that time frame is going to be 18/2, and that's 9 m/s, so the first distance is 108 m.

What about the second distance where it's going for a constant speed for 25 seconds? So it's going at 18 m/s at this point, for 25 seconds, so that's 450 m for the second distance.

And for the third distance. It's decelerating to zero, and since the numbers are the exact same, you're going at 18 m/s and your acceleration is the same but opposite, so it too is 108 m, so then you just add all of these numbers together, and it's 666.

Part B on this problem: what is the average velocity? If you want the average velocity, do you find the final displacement minus the initial displacement, so the change in displacement, and then divide by the change in time? Approximately 13.6 m/s.

How about a rocket being fired vertically?

The Perfume Problem

The rocket is fired vertically upward with an acceleration of 20m/s^2. After 25 seconds, the rocket shuts down. And then the rocket continues as a free particle until it reaches the ground. What is the maximum height? What is the total time in the air? What's the speed just before impact? The velocity at 25 seconds is 500 m/s. At 25 seconds the problem is like launching a rock from a cliff, which only has velocity. So basically we are going to find our S_{0} on our new start of the problem. In that time period, we have average velocity is 500+0 all over 2, and you were traveling for 25 seconds. So our S_{0} is the first part where we start where the acceleration goes to gravity instead of the rocket's propulsion system. So it's 62.50 m or- average velocity times the time.