HW 24: Up, Down, Splat!

Melissa's science class is having a contest. The contest is to see who can build a container that will keep an egg from breaking when dropped from the school window.

Melissa is quite confident about her contraption. She leans out the window, which is 25 feet off the ground, and hurls her egg container straight up in the air with an initial velocity of 35 feet per second. (Consider velocity upward to be positive.)

Assume that the egg container's velocity is affected by gravity in the usual way. That is, the velocity decreases by 32 feet per second for each second the egg container travels.

1. How long does it take for the egg container to hit the ground?

2. At what speed does the egg container hit the ground?

Velocity is Speed with Direction

In class we have looked at several scenarios dealing with acceleration and velocity. We have used the following formulas:

h = -10t^2 - 30t + 200 from Look Out Below
h = -16t^2 - 7.85t + 65 from HW22: Big Push
h = -16t^2 + 50t + 90 from HW23: Problem 2c

What is the significance of the sign of the velocity term? - 30? - 7.85? + 50?

Is the sign of the velocity term for our Ferris wheel problem always negative (- 7.85) as seen from HW22?

HW22

Today we applied OUR physics equation for distance travel to our Ferris wheel problem.
We calculated the fall time including the initial velocity (speed) of the Ferris wheel. We then calculated the fall time with NO initial velocity. What did we observe? Why?

Does it matter whether or not the Ferris wheel is moving?

Look Out Below Revisited

Today in class we discovered the following equation:
height of pillow = -10t^2 - 30t + 200
Can anyone explain where the numbers came from?

And how does this relate to HW22?

Comments, ideas, suggestions?

What is the path of the diver's fall from 3 o'clock???

Today, we had some very good discussions about the path of the diver if he fell at the 3 o'clock position. We recently learned that the circular motion of the ferris wheel is applying a "force" or as Ms. Kovacs said, a velocity. This velocity is in the direction of the tangent to the circle. Here is a link to see the tangent as the ferris wheel makes revolutions.

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=148

The red arrow is the velocity (tangent to the circle). Does anyone know what the yellow and blue arrows represent?

Does this clarify the path of the diver if he is let got exactly at the 3 o'clock position?

Jena6 POW

Our Jena 6 POW is due Tuesday, Nov. 20, 2007.

Please use the comments to discuss the POW. What have people tried? What seems to work? What type of math is important to solve this problem?

Notice that the write up is slightly different than the previous POWs.

Here are some links to websites about Jena 6.
http://www.freethejena6.org/
http://www.democracynow.org/print.pl?sid=07/07/10/1413220
http://sports.espn.go.com/espn/news/story?id=3030458

As you may have experienced before, there are two sided to every story. We have to try to understand the bias in things we read.

Here are some more links about Jena6 that are trying to provide the "truth".
http://www.thejenatimes.net/Chronological_Order_of-Events.pdf
http://www.csmonitor.com/2007/1024/p09s01-coop.html
http://www.talkleft.com/story/2007/9/23/17283/0387
http://friendsofjustice.wordpress.com/2007/07/02/ineffective-assistance-of-counsel-what-blane-williams-should-have-known/

What do you think really happened?

Here is a link to the POW.
http://www.jonescollegeprep.org/ourpages/auto/2007/11/8/1194539748772/Jena%20POW.doc?rn=6573408

Look Out Below!

In class we were trying to work on this problem.

Maxine sees a pillow falling from her window. She know the pillow is falling at an acceleration of 20 ft / sec^2. She also knows that the pillow is traveling at an instantaneous speed of 30 ft/sec when Maxine saw it.

1. What is the instantaneous speed of the pillow 1 second AFTER Maxine saw it? 2 seconds after Maxine saw it?

2. What is the average speed of the pillow for the first 2 seconds AFTER Maxine saw it?

3. How far did the pillow fall during the first 2 seconds after Maxine saw it?

Maxine knows the sidewalk is 200 feet below her window.

4. How long did it take for the pillow to reach the ground from the time Maxine saw it?

5. Find a general expressions for the height of the pillow t seconds after Maxine saw it.

Please post your answers, questions, suggestions in the comments.

HW20: Initial Motion from the Ferris Wheel

For today's warmup, we looked at problem #1 with the skateboarder and the merry-go-round. The skater actually moves in a straight line, which happens to also be the tangent line to the circle at that point.

We defined the tangent line to be a line that crosses the circle at one point, and the tangent is perpendicular to the radius at that point.

To test this at home, you can tie an object (remote control, stuffed animal, a balled up sheet of paper, etc.) with string. Swing the string and object around yourself in a circle. Then let go of the string, and watch the object fly. You should notice that the object continues in a straight line (except that it sinks to the ground). This straight line is tangent to the circle.

Problem #2 asked us to apply this to our Ferris wheel problem. The diagram illustrates the path the diver takes after being released from the 4 o'clock position. Notice the initial path is the tangent to the circle, but then gravity causes the diver to fall.

The Analytical Rakim...I Know You Got Sine

Its been a long time, I shouldn't have left you
without a math POW to get you
think of how many math problems you slept through
times up, I'm sorry I kept you
thinking of this, you keep repeating you missed
concepts and formulas from the wheel of ferris
And you sit with your calculator, hands on the buttons soon
As you hear it, pump up the volume
Hurting your brain, until you hear it blow
Then plug in "y equals", cause here it goes
Its a 4 letter word when its heard it reminds
trigonometric functions (you got it) sine
Nine degrees a second like angular speed
height to the center, thats what we need
when the wheel is moving, you can't get stuck with
the diver's position, so you can come up with
a time to fall, past the 3 o'clock, the wheel will go
Plus knowing that the cart left a long time ago
It can be done, but only you can do it
For those that understand, then clap you hands to it
You start to think, and then you sink
onto the platform and in a blink
You're calculating, looking at the intersect lines
You tell the diver to jump at the right time...
You got sine

You got it (4x)
I know you got sine...

Picture a graph, the points are empty
A grid like this might tempt me
To pose, show my skills and my phat TI
grab a clock like I needed PI
but i'll wait, cause i mastered this
let the others go first so that the groups dont miss

............sorry......i just had to get that off of my chest......