math, 144 ft buildings, magic balls, and open manholes

Today we were discussing the magical bouncy properties of magical bouncy balls and breaking some of the laws of physics.

And by that I mean we were discussing quadratic functions practical-applications-word-problem-stuff.

The problem:

A ball is thrown from the top of a 144 ft. building. The ball follows a trajectory. The height (in ft.) reached by the ball after t seconds is given by the QF H(t) = 96t - 16t2
a) How high did the ball reach?
b) How long did it take to reach that height?
c) Where is the ball after 5 seconds?


This is the practical-applications-word-problem-thing. Because throwing a ball from a 144 ft. building is totally practical.

I'm okay at quadratic functions, but add a building, a bouncy ball, and a stupid person in the equation (hehe see what I did there?) and my brain becomes a puddle of liquefied crap. Mushy, gross, and useless.

Anyway. If you convert the equation from the general form to the vertex form, you'll get -16 (t - 3)2 +144 which means the ball will be 144 ft in the air at 3 seconds if thrown from the ground.

Which is impossible unless the ball is thrown by a naked, hunky dude with a fake tan and blond hair with superhuman powers. Yes, the blond hair has superhuman powers.

NAKED HUNKY DUDE HOLDING A BALL OMG.

But since the problem said the ball was thrown from the top of a 144 ft. building, it was thrown from the top of a 144 ft. building--not from the ground. (So there's no need for the naked hunky dude. Sad face.)

 So since the maximum value is 144, I answered 144 ft. for question A. And since the ball was already at 144 ft., I answered 0 seconds for B.

Now question C is the bitchy question.

If I'm correct (which I'm probably not), the ball hits the ground after 3 seconds. After the ball hits the ground, of course, it will bounce. And the parabola for the next bounce will obviously be a different equation.

Unless...

Now that is creative thinking.

But as I've predicted, I was wrong in the first two questions so my awesome open-manhole theory is also wrong and that is sad. And because our Algebra teacher is old and has the wrong idea of what we think is "fun" and "suspenseful", she gave the last part as a homework. She told us to really think about the problem. To pay attention to details or something like that. She thought the "suspense" would motivate us to take this thing seriously. We're all just hoping that the dude holding the ball falls. Now that is suspense.

And if any of you are in QC/Metro Manila today or tomorrow (Haha fat chance), you can go to the Bandfest! COME ON I NEED TO SELL THE FUDGING TICKETS AND IT'S GOING TO BE AWESOME 'CAUSE IT'S CALLED "FIAT LUX" AND DOESN'T THAT JUST SOUND AWESOME. Here's a trailer thing. You could choose to not watch it, but you'll miss 1/576 465 819 of your life. It has never before seen text from Genesis.

Apparently, God said "Bandfest like you've never seen before." Must read the Bible more.

COME ON BUY MY TICKETS. IT'S FOR GAWAD KALINGA AND SEFI. THINK OF THE POOR PEOPLE OF MY POOR COUNTRY.



Lesson learned: Muscle-y people who have magic blond hair are automatically good at physics and math. Also, Ctrl+B would make your font bold.