Pedro the Pi-Rate Panda and The Black Spirit.

The waves plundered, the skies thundered and the ship floundered like a fish out of water. These men have been tried through great storms, but never as much as this storm was. Pedro sat in his cabin as the men struggled to stay on board trying to keep the sails up, and the ship from sinking. They would hate their captain for this.
Pedro, also known as the black marked pirate, became captain of The Black Spirit two years before. The men believed Pedro brought on a curse of bad luck. The Black spot is a curse to pirates, and Pedro was covered in black spots. Kuro kuro told them he was covered in white spots. Kuro never had bad thoughts towards Pedro. Even with Pedro being the overbearing pirate that he was, Kuro kuro seemed to be the only one who understood him.

The following morning, the sun peeked through the white clouds. The sky turned blue. The air smelled of the salty sea. Pedro came out of his cabin to sound the bell to wake the men, who’ve only been sleeping for two hours since the storm. Pedro was the only person who knew where they were heading. He has never trusted anyone since that terrible day on Hugwarts Island three years before. He blamed himself for his mother’s disappearance and Hisoka’s death.
Pedro was searching for the mystical treasure that has been taking him far out to many seas in the past thirteen years. Pedro was just a little panda when his father left. His father told him of the adventures of people in search of the treasure and mysteries lost out at sea. When his father left, parts of the stories left with him. Pedro remembered hearing his name once at the docks along the island. When he asked the men just laughed and pushed him away.

The Black Spirit pulled into Chainrule Island. “Arr, me hearty, ya’ll be gettin off this ship and gettin the supplies fur tomorrow” Pedro yelled. The men thought they were there for supplies, Pedro had other intentions. He was looking for a man. A man who dominated his father’s stories and Pedro’s childhood dreams.
Pedro and Kuro Kuro walked into the pub. It reeked of rum and drunken pirates. He went to the bartender and said “I’m lookin for a man”
“This boy here is lookin for a man!” The men laughed, irritating Pedro.

“ I’m looking for Jackson Hawk” asked Pedro

“What ye be wantin’ with ol’ Jack?” the bartender questioned

“ He has something of interest” Kuro said, before Pedro could answer

“JACK! This panda here be lookin’ for ya”

A man at the back of the room walked out. The drunken men became silent. The only person in the room anticipating his arrival was Pedro. He was finally going to meet the famous Jackson Hawk. Jackson appearance was just as he imagined when he was young. Jackson with his long hair, beaded beard, ungraceful saunter caused by his pegged leg, and his famous hook for a hand. Kuro, being the gentle person he was, seemed frightened.
“Are you Jackson Hawk?” said Pedro. Breaking the silence.

“Who be askin’?” answered Jackson.

“My name’s Pedro the Pi-rate Panda”

“And who sent you here?” said Jackson with a striking interest in Pedro.

“No one. I’ve been looking for you. You have something of interest to me.” said Pedro

“Aaahhee. I think me know what ye been lookin for, but what’s in it for me?” said
Jackson being the greedy pirate he was.

“Well you know what you have and what it leads to. I have a something you need in order to get what your map leads to” said Pedro, looking at a confused Kuro.

“And how do you know that I’d be needin this thing you say you have?” said Jackson, while drinking rum

“Because I have it and I also knows what it leads to” replied Pedro in an arrogant tone.

“How did ye happen to come across this piece and my name?” Jackson asked.

“My father told me of you and your stories”

“Arr, Yes ye father be knowin all about that”

“You knew my father?!” Pedro said in surprise.

“Yes I knew the man. A good man, yer father.... Well I guess we should be goin now?” Jackson got up from his chair, taking his rum.

“Goin where Jackson? Pedro said still sitting in his seat.

“We’ll be gettin on our way to find where my map and your necklace be leadin”

“And how do I know for sure you have it.” Pedro stood up following Jackson.

“Because I have it” Jackson says sarcastically mimicking Pedro’s voice,

“Show me!” Pedro said, stopping Jackson in surprise.

“You don’t want to be doing that young one. I told you I’ve got it then I got it! Savvy?”
Pedro put down his sword.

“ Very well then, lets go, come Kuro. We’ll set sail first thing in the morning” Pedro and kuro leave the pub behind Jackson.

Kuro whispered in Pedro’s ear “You’re actually trusting this man? You don’t trust anybody!”
“Who said I trust him?” answered Pedro in a contradicting voice, worrying Kuro.


The next morning...
“ALL RIGHT MEN! GET UP! Set sail, get moving!”

“Captain? Kuro Kuro is not to be found aboard the ship” said one of the buccaneers.

“Well then where is he?” asked Pedro

“We don’t know, the men, they not be seein him since last night wit you cappin’?”
Jackson came out of no where “ Oh well, I guess we be leaving him then... It’s time now Pedro, set sail!”

“Did you have somethin to do with this?” asked Pedro moving towards Jackson.

“Nothing, nothing of the sort. He’s probably chasing rats down below.” Jackson replied.

“EVERYONE. We’ll not be leavin’ until we find Kuro!”
One-eyed Sam came out from below deck with Kuro Kuro shaking trying to escape from a potato sack.

“All right men, lets get moving. SET SAIL”

“Pedro! Ol’ Jackson here is a SPY!” Yelled Kuro Kuro. “I saw him talking to one of the Queen’s men late last night!”

“Arr, that aint the truth! That nosy lil weasel saw me talking to some person I’ve never seen before! I simply told him directions. When I saw him, he freaked so I simply put him in a potato sack. No harm done, see.”

“LIAR!” yelled Kuro, grabbing a sword.

“Shush! You lil rat! It’s the truth. Swear on my heart matey. I’ve ne’er e’en knew we have a queen” said Jackson trying to defend himself.

“Alright Jackson. I’m allowing you to come, but if I come across something that questions my trust it’s the plank for you!” Said Pedro, while hesitating thoughts ran through his head.

“Yes Pedro. The plank. It’s not the first time I’ve done that. Bloody traitors!”

“That’s very reassuring Jackson” Kuro said

The Black Spirit left Lilly Island. Not thinking of what or who followed them

Three days later, they still didn’t come anywhere close to where they were heading. The crew didn’t care because they never knew where they were heading anyway, they only listened to Pedro’s directions. Only this time Pedro would join them in taking directions. The crew sang as they worked.
“Lo Di Hi - Hi Di Lo . We’re gonna find us some treasure and take it all home”

“Where are we Jackson!? You should have let me read the bloody map!” said Pedro.

“I know where we are mate! Just trust me- you probably wouldn’t even be here without me!”

“I’m sure and certainly wouldn’t be lost” said Pedro.

“And how do you know we’re lost? Can you read this map!” he said throwing the map in Pedro’s face. Pedro read it trying to decipher it.

“Didn’t think so mate” Jackson said, again irritating Pedro. “Well at the rate we’re going we’re never gonna get there any faster. Queen Hopra is following us. Their ship is much faster than ours!”

“Don’t worry I sent them to an island directly east from the island with the treasure. We be headin’ straight for it down south!” Jackson said reassuring Pedro.

Kuro came up deck with a curious untrusting look on his face. He noted Jackson’s pegged leg, eye patch and hooked hand. Kuro asks “How did you get you pegged leg?”
Jackson replies “ There was a storm and I was swept overboard into a pool of sharks. Before they pulled me in one of’em bit me leg off.”
Kuro asks “ Well then how did you get your hook?”
“I was caught stealing from a merchant. Them officers arrested me and chopped off me hand!”
“And how did you lose your eye?”
“ A seagull dropping fell into my eye!”
“You lost your eye to a seagull dropping!” said Pedro amazed.
“Ayy, yes it was my first day with a hook for a hand...”

Two days later, Jackson said they were near the island of Leibniz. “We should be gettin there in a few hours.” Jackson told Pedro. Pedro was relieved to find that he could actually trust Jackson. However, Kuro still didn’t trust him.
About an hour later, the island is in sight. Pedro’s ship must’ve only been going 1.38 m/s, while the Queen's ship was going faster at 2.22 m/s. It was a race to the treasure that both the Queen and Pedro desired.

To be continued...

Problem
When The Black Spirit is 10 kilometers directly north of Island. Queen Hopra’s ship is 15 kilometers away from the island. At this point the ships are within cannon range of each other. What is the distance and rate of change of the distance between the ships at that point?

Pedro the Pi Rate Panda, Part 1

Introduction
.
First off, if there are any problems with the characters’ names (copyright laws, you don’t like them, etc.), please let me know. They’re (sorta) negotiable =). I gave a name to Pedro’s little friend, and if you don’t like it, again, please let me know. I named him “Kuro Kuro, the Math Genius”! The name’s after… guess who?? I just wanna say that this is a bit lengthy, and I apologise for that. It’s because this is the first part of the story, so I have to introduce the characters and get the plot going.

For those who visited the blog the first time, this is one of Mr. Kuropatwa’s AP Calculus class’s projects. We are supposed to publish a story about Pedro the Pi-Rate Panda, whose name we agreed on during a class discussion. Pedro will go through the adventure of his life, and along the way are calculus problems that need to be solved. Each week, one of the students will continue Pedro’s adventure, from the “part” written prior by another student. All of us must also post the solutions for our problems, which will be posted in another blog. The link should be at the side.
With this project, we are aiming to have fun, be creative, and at the same time cover calculus concepts that we’ve learned throughout the year! So please regularly visit here, and join us as we carve the life of Pedro the Pi-Rate Panda =).


It was one of those days when the sun’s rays seemed perfect. Birds were chirping, the trees mildly swaying, and the grass beneath looked greener than it had ever been. It stretched miles and miles, broken here and there by bunched up flowers of all kinds. Thousands of colours before the eyes, and in normal days it would look chaotic. But this was a different day.
It didn't change, Pedro said to himself.
He left the Hugwarts Islands 10 years ago. Pedro tried to convince himself that he'd go search for his father, who left when he was still little and cute. In truth, Pedro wasn’t even half-concerned about his father. He wanted to change his purposeless and mundane life, to one full of excitement. And so Pedro left. After all, he was a teenager, and every living creature, save a few, had thoughts like his. An ordinary being would not act on his thoughts, but Pedro was not like that at all. He was one of those few who knew for a fact that thoughts, valuable as they are, aren't worth much unless coupled with action. This time, however, the rolling green meadows with flowers and tress, the butterflies and bees were calling him. He didn’t know why, but it almost felt like something was dragging him. Daydreaming about the sight before him, Pedro suddenly tripped and fell on his face.

He stayed there, face down, for a few seconds, when he heard someone giggle not far off. The noise stopped abruptly. Whoever it was has been following Pedro for a while, and the panda knew of it. He decided not to confront the follower just yet.

As he stood, Pedro saw someone coming. The melodic chirping of birds, swaying trees, flowing water, were ignored. Heart pounding. Dub dub. Dub dub. Pedro knew who it was. Hisoka. He was one of only about ten white tigers left in the world, adored and respected by everyone despite his age. Every creature knows of someone who, for some unknown reason, seemed to be a magnet to others.
Pedro didn’t know what to do. He was arguing whether to hide from his childhood friend, or face him. Sure, they were best friends, born on the exact day, growing up together, eating on the same dishes, but Pedro left without notice. He thought of the short note he left. It read, “I will be gone for some time. I’m looking for dad.”
That was stupid. Pedro thought, pounding his head with enormous paws. STUPID!
Half an hour after he left his house, Pedro heard the most terrifying cry in his life. The roaring was as loud and as harsh as a tiger can make it. It sounded of glass breaking right beside the ears, magnified by a hundred, longer by a hundred. Pedro knew it was from Hisoka, and it seemed to say, “and I thought we were friends…” Most would find that cry too dramatic, but what could be expected of Hisoka? Not a day passed when the panda-tiger duo didn't spend time with each other. Not a day passed when Pedro didn't poke fun on Fishy, the cute little turtle, for his one shorter leg thing; not a day passed when he missed the opportunity to prank big-old-CowCow the cheesemaker, while Hisoka stayed behind to take the blame and fix the mess.

The majestic figure of the white tiger appeared closer and closer to Pedro. Then it stopped. About fifty metres away from Pedro, Hisoka stared, dumbfounded. He stood with confidence, but that confidence, it seemed, was shaken.
“So you’re back,” Hisoka said.
“I… I’m sorry,” answered Pedro, looking down.
Hisoka started to walk towards Pedro, gliding on green grass with a King's grace, until the two were face to face.
“Pedro,” the white tiger said, “why are you here?”
“I didn’t know better, Hisoka.. I really didn’t… I’m sorry… don’t make me cry…” All of a sudden, Pedro was hit on the head with massive paws, falling flat on his face.
“What the heck was that for?!?” then Pedro, once again, was beaten down to the grass that before he loved and now hated.
“I’ll make you regret the second your father laid eyes on your mother!” said Hisoka. “You should not have left your house you dimwitted dodo head!” All that was regal about the tiger was gone. “You left your mother, Mrs Regina Orangina Lupin III, alone!” The beatings kept coming. Hisoka rambled on, anger replacing the faint joy that was in his eyes when he first saw Pedro. “You left ME alone you…” Anger turned to longing, like that of a brother to a brother. He started sobbing. The assault stopped. A pause went on for seemingly forever, when Hisoka said, “I missed you Pedro, that’s all…” Hisoka's little speech was interrupted when, out of nowhere, tiny hands grabbed his tail and he was spun around like a ball of yarn. It was the follower.
No one could have believed such a small thing could even lift an apple, but there the creature was, acting like a cowboy with his ropes. It threw Hisoka into the air, far away, nearly out of sight. Thud. Hisoka fell. Pedro got up, in shock, and even more so when he saw how far Hisoka had gotten.
“HI!” said the creature. “My name’s Kuro Kuro, and I want to be your…”
“What did you just do?! Oh man… Hisoka… I’ll be there don’t worry…”
And with that, Pedro ran towards where his friend landed.
“…friend…” Kuro Kuro continued, nearly without spirit as a deer’s carcass.




Pedro ran after Hisoka. When he caught up, he reached for the tiger and helped him up. Blasted… thing.
“What was that, Pedro?” asked the tiger, all hostility towards the panda now gone.
“I have no idea. MY GOSH I’m so mad!”
“No matter, Pedro. We have more pressing things to worry about.” The look of wisdom was back. There were those who tried to be wise, and those who just were, and one can never be taken for the other. Hisoka was a prime example of the latter.
“Is there anything wrong, Hisoka?” Frowns formed on Pedro’s face.
“Well, about an hour ago, five large humans, dressed in fancy suits, came to your house. They were asking for you, and Mrs. Regina Orangina Lupin III said she did not know of anyone named Pedro.” Pedro’s frown deepened. He was concerned about those uninvited guests, but was more troubled by what his mother apparently said.
“In any case,” Hisoka continued, “you should leave. They brought a declaration from Queen Hopra Winfrey, the Mistress of All The Hugwarts Islands, demanding anyone who knows anything about you to report to her guards. She wants you, Pedro, and what Hopra wants, Hopra gets.” Hisoka’s tone was almost too cold; too matter of fact.
“What could I possibly have that the Queen would want? I have nothing, Hisoka, none.” Pedro was almost pleading. Other than his escapade, he had done nothing that could even slightly interest Queen Hopra.

Queen Hopra was popular among her subjects. Besides her significant weight loss, she had done many things worth noting. Queen Hopra, whose ancient title included being the Mistress of All The Hugwarts Islands, led her kingdom to prosperity. "The forgotten wart-plagued-hogs place," as it was branded before, was transformed into the center of commerce and culture of the world. The Hugwarts Islands was the place to be, the source of popular culture and dictator of what went on in the global theatre. Among so many that Queen Hopra raised from poverty to fame was Tom Hortons. Mr. Hortons was just a regular neurosurgeon, earning three eggs a day, when he was discovered by the Mistress of All the Hugwarts Islands. He would become known as the founder of McStarrybucks, a global fastfood chain/tv station. Hopra was also known for giving away lots of expensive donkeys, the most common transportation in the land. In one of her parades, Queen Hopra was known for giving away a thousand donkeys, pointing at someone randomly and saying, “you get a donkey, you get a donkey, you get a donkey!” Surely enough, those people got donkeys. But that was the peak of her glory. She soon started to gain weight again, and became grumpy. She reinstated slavery, and not long after that, the Queen personally wrote particularly cruel declarations. Soon, Hopra was either extremely loved for what she had been able to do for the Hugwarts Islands, or extremely hated for what she had become.
“I don’t know what they want, Pedro, but as soon as those humans left, I went to search for you, and there we met at…” Hisoka’s voice drifted in Pedro’s head. None else seemed more pressing than that a grumpy queen, Cruella Devil incarnate, was hunting for him. He cut his friend off, “Hisoka, we must go to my house. I need to know what’s going on. Well, and say hi to my mom too.”

As they reached the house, an old panda opened the door, who appeared to be in horror, gasping, sunken eyes staring straight ahead at Pedro. Mrs. Regina Orangina Lupin III was, at most half of what she was, before Pedro left ten years ago. Tears started to well in her eyes, when she was grabbed by her son and was hugged with enormous arms.
“Forgive me, mummy Mrs. Regina Orangina Lupin III.” Pedro’s voice was as steady as a rock. My gosh, she’s thin. “I’m happy you’re alright,” Pedro continued, almost mechanically.
“Well,” Mrs. Regina Orangina Lupin III began, with the grace of a princess that she’s always had. “I must cut our reunion short. You have to leave this town, this country even, NOW!”
“But mum..”, Pedro was taken aback by the sudden outburst of emotion.
“I said now!” Her eyes were even better at giving commands than her words. “I know there are people watching this house at this very moment. Those five that visited this afternoon are still here. I know this, Pedro, trust me. LEAVE! NOW!”
“MOM! WHAT ARE THEY AFTER?! COULD YOU PLEASE JUST TELL ME?!”
“Pedro, that necklace your father gave you….” when all of a sudden, the front doors were kicked open, splitting into countless shards.
“PEDRO, RUN!” Hisoka said. “I’ll stay here with Mrs. Regina Orangina Lupin III.”
“Hisoka…”
Hisoka shot Pedro a look that made the panda stop. “I was your friend since birth, and even when you left me, we were still friends…”, the eyes seemed to say. “I would gladly face these monsters for you.” All of these were in Hisoka’s eyes. It started to rain.

Pedro ran outside, through the back doors. He ran and ran, trying to go faster. He came within sight of the donkey he used when he went home. Pedro ran even faster, rain on his face, until he reached the donkey. As he hopped on it, he suddenly realized that he forgot his McStarrybucks coupons, so he galloped towards the house. Pandas' cravings for McStarrybucks Whopping Good Frapuccino had to be quenched. About three kilometres away from the house, Pedro stopped. The whole town was on fire. The rain did little to stop the blaze. Pedro was in shock. I’ll make them pay. Patience, Pedro. You must wait. He was scared, but he also well knew there was nothing he could have done. The Queen wants something, and she’s willing to use violence to get it from me. That forces me to believe she should not have it. The necklace dangled from Pedro’s neck, shining despite the rain. He finally decided to push the donkey hard away from the town. Pedro’s stamina was tested. He felt as tired running, as trying to stay on the donkey. He fed his tiring body with anger and determination, and the combination of the two made him keep going. The donkey kept galloping until Pedro felt he was safe. He sighed. My gosh, gladly it's now done.. BOOM!
The donkey stepped on a mine and exploded. Pedro, luckily, survived the blast. From a distance, he can see a battalion of soldiers coming towards him. Leading them was a man on horseback, wearing full knights’ armor, with a helmet that had five coloured feathers sticking out. He was holding something out that Pedro couldn’t quite make out. As they got closer, it seemed clearer. Pedro shivered. He could not believe what he was seeing. The officer was holding out Hisoka’s bodiless head. “Give up, commoner! If you don’t want to be like your friend!”
Pedro just stood where he was, staring. He wore a blank expression. Neither grief, nor anger was on his face, but pure unknowing. It was as if he was just born at that instant, clueless about everything and anything he saw, or heard, or felt. The soldiers came nearer.
Something touched Pedro’s paws. It held Pedro tighter, and all of a sudden, he and the creature were on air, flying, getting away from the soldiers. I will not leave you alone, Kuro Kuro thought. .



Pedro sat on a rock beside a river. They were far away from the soldiers now, even far away from Hugwarts Islands. Tears flowed from Pedro’s eyes. He was completely serene, nothing but the swaying of the trees behind them and the river flowing in front could be heard. He was just staring on a lone red rose on the other side of the river, expressionless, but for the flood of tears from his eyes. He’s been like this for two hours, Kuro Kuro thought.
Seemingly out of nowhere, Pedro said, “Thank you…”
“Kuro Kuro’s the name”
“Thanks, Kuro Kuro.”
Pedro wore a different expression now. Not grief, not anger, but acceptance. His speech was so cold, and so contradictory to how he looked.
“I will have my revenge.”
Clear and simple. Pedro was alone, save the little creature sitting beside him. He was not going to ask for help. It was his dilemma, and he had to solve it. His course was set. The wheels of vengeance have started to turn. The road to retribution began for he who would become known as Pedro the Pi-Rate Panda.

TO BE CONTINUED....


PROBLEM:

This problem pertains to "Pedro's Escape", as seen in The Revelations chapter of the story, beginning as soon as Pedro leaves the house, and ending when the donkey dies. Given below are six graphs, labeled A-F. Identify Pedro's position-time graph, velocity-time graph, and acceleration-time graph. Justify your answers.

Notes: Assume that pandas and donkeys have tremendous endurance. Their velocities are comparable with each other.

SOLUTIONS AT: http://pandasolutions-apcalc06.blogspot.com/2006/11/pedro-project-part-1-solution.html