Pedro's Love Problem

Pedro’s peripheral vision seemed to have failed him. He no longer saw anything around him. The Pi-rate panda only saw the treasure that he was closing into. He was vaguely aware of the evil Queen Hopra that was trailing behind him. I wonder how this treasure will help me, Pedro thought, daydreaming about what he can do with this fortune. He can get married to a beautiful panda; of course, it’s difficult to find a panda mate. They’re endangered, after all. Maybe if there was enough, he could overthrow Hopra off the thrown. King Pedro…it does ring a bell. I could have a dozen donkeys pulling my dozen-donkey sleigh…and…BAD PEDRO! You’re supposed to be looking for your father! The panda started to beat himself on the head in rapid succession.

“Pedro, sir! LOOK!” Kuro interrupted Pedro’s self-scolding. He pointed towards Queen Hopra’s ship. One of her hideous beaver henchmen pointed a large canon towards the Black Spirit.
“What should we do Pedro, sir?!” Kuro was near hysterics.
“Let her blast it!” Pedro replied, in a somewhat uncaring tone.

As if on cue, the entire Black Spirit heard the sound of a cannonball launched from Hopra’s fancy, million-dollar mahogany ship.

“We goin’ ta die, mate!” Jackson Hawk screamed and ran up to Kuro and hugged to the little being.
“S-s-suf-suf-o-ca-tiing…!!” It was impossible for Kuro to escape Jackson’s iron grip.
“First me leg, then me hand, then me eye! NOW MY HEAD! I can’t replace me head!”

All but Pedro aboard the Black Spirit threw themselves on random parts of the ship and said sorry for all the bad things they have done.

“I think he gone mad!” Jackson exclaimed, still holding on to Kuro.

The Black Spirit crew anticipated for the cannonball to hit their ship. A few seconds later, they heard a plop sound. The cannonball wasn’t even close to their ship. It had landed into the ocean for the poor sharks and dolphins to find. Everyone was shocked, including Hopra’s crew.

“Lo Di Hi – Hi Di Lo! The cannonball took a dive and we’re all still alive!” The Black Spirit crew sang, busting out some of their dance moves.

Queen Hopra’s jaw dropped. She was obviously not impressed by the showmanship of her idiotic crewmen. She was so angry that she didn’t even wait for the beaver to walk the plank. Hopra threw him off the ship was her own hands. Pedro smiled and waved to the seething Queen, then turned to face his own crew.

“Full speed ahead to Leibniz Island!” Pedro was a strong leader despite his adorable panda cuteness. Everyone on the ship went to work straight away.
“How did you know that the Queen wouldn’t be able to shoot us?” Jackson questioned.
“Hopra failed Calculus and Physics when she went to Queen School. I knew she wouldn’t be able to catch us. Even if she could, she wouldn’t have known. Her crew obviously isn’t much help to her,” Pedro answered. “No more interruptions, I’ve got treasure on my mind.”
“Pedro, sir. Look over there,” Kuro tugged on the Pi-rate panda’s paw. He pointed his paw towards the island.

There was an eerie golden glow surrounding a box. It was the treasure box! The crew was ecstatic but then the latch was unlatched and it opened. The winds grew stronger and the Black Spirit was getting pulled into the box. Actually, everything that was within a 20-mile radius of the island was getting sucked into the vortex.

“What’s going on, Jackson?!” Pedro finally showed some panic across his face.
“Me not sure, mate! We getting’ sucked in!” The experienced pirate yelled over the gusts of wind.

Pedro no longer saw solid objects around him. All he saw were blurs of blue and his crew’s faces. Then he was falling. Him and the ship were plunging down towards…something.

“WHY GRAVITY?! WHYY?!” Pedro was definitely in hysterics right now.

The ship crashed into the earth, creating a large crater. Amazing enough, after the fall, Pedro was still in his right mind. Assume he was.

“The forecast for today is VERY HIGH!” Pedro heard a high-pitched female voice.

He looked around and saw a little human girl talking into a microphone and a camera recording her.

“This Valentine’s day will be full of love! For those cynical beings out there, watch out, or the love-panda will come and shoot you with the bamboo stick of LOOOVE! This is today’s Valentine’s report. Have a good one!”
“Valentine’s day? Today?” Pedro looked around him and sure enough, he saw pink and red everywhere. There were hearts on the windows of stores and love songs playing, his crew was dancing with pandas. “Crew dancing with pandas?!” His eyes didn’t fail him today, his crew was teaching the pandas (they're not so endangered after all) how to dance the Sine Dance.
“Sine, Sine, Cose, Bust-a-Move, Cose, Sine!” The Pi-rate panda was so surprised by the antics of his shipmates that he almost jumped when he felt a tap on his shoulder. He turned around and met the eyes of a female panda. She looked strangely familiar to him.

“Pedro, is that you?” She asked.

Who is this? Pedro thought to himself. I’ve met many creatures on my travels. But this she-panda…I remember! I met her about a month ago at the Panda dating service. There’s not many of us, we had to meet somehow! “Petriva, my dear! It is I, Pedro!” he said and stuck his paw out. It was ignored, however, since Petriva jumped on him, kissing him desperately.

“I was so sure that we wouldn’t meet again! But here you are! We can get married now!”
“Marriage? Who said…” Oh darn, I did it again, Pedro thought. Too many poison berry cocktail…again. Suddenly someone spread the two away from each other. It was the newscaster from moments before.
“Hey there lovebirds! Test your love by participating in the game show…LOVE OR NO LOVE! We have a marvelous prize, a Mitts-Cord-Donkey!”
“That’s the most expensive donkey around! Pedro, we must go!” Petriva begged, she really had a taste for expensive donkeys.
“I don’t know…”
“Come on, it’s Valentine’s day! Win your she-panda the donkey she deserves!” Little girl said enthusiastically. Pedro didn’t know what happened, but he was now blinded with the spotlight. He looked out into the audience. Not surprised, he saw his crew members in the front row with a “GO PEDRO, KISS THE GIRL” sign.

“Valentine’s day is the most important holiday on Riemann-Sum-where city. Just for today, we are going to find out if these two lovely couples really know each other.” Little girl said to the audience. “Pedro the Pi-rate Panda, what is Petriva the Panda of Pop’s favourite ice cream?”
“Uhh…pizza?” Obviously the question was wrong…in consequence, pie was thrown in his face.
"Queen Hopra of Hugswart, what is Benny the Beaver’s favourite food?” Hopra also crashed into Riemann-Sum-where city as she was in the vortex-sucking range. The beaver was also sucked in, just before a sea otter ate him.
“Beavers…” Again, wrong. A bucket of black ink was poured on the regal being’s head. This went on for about half an hour. The four creatures that answered the questions got them all wrong and were punished for it.
“Petriva, what is Pedro’s most prized possession?” Little girl asked, annoyed on how these couples were so incompatible.
“The necklace his father gave him,” Petriva replied.

Something clicked in Pedro’s head. I never told anyone that, he thought. This is not right.

“How did you know that, Petriva?” he asked her with suspicion in his voice.
The she-panda looked surprised. “You told me of course…”
“No, I didn’t tell anyone about it. You’re up to something. Who do you work for?”

The game show host was overjoyed by this revelation. The viewers love drama.

“She works for me,” Hopra said trying to look menacing for the ice cream cake on her head made it seem less scary.
“Hand it over, Pedro. There’s no escaping now.”
“It’s true, Pedro. That dating service was a hoax,” Petriva then took off her mask. She wasn’t a panda at all! She was a mole rat!!
“Pedro, sir! Over here!” Kuro and the Black Spirit crew were starting to leave the building. Pedro found a rope, conveniently hanging from the ceiling and made his way to his mates.
“RUN!” he said when he saw Hopra, the beaver, and Petriva, making their way towards them. When they made it outside, Pedro found a brand new ship to replace the old one.
“The panda dancers made it for us. Real bamboo!” Kuro said.
“What is that?” Pedro asked pointing to a piece of wood in Kuro’s tiny arm.
“It’s an iLog. If I press my ear against it, I can hear the Sine dance song and the Quotient law song!”
“Oh yeah, I forgot, we’re being chased by the Queen!” Pedro wasn’t too worried about being caught. Hopra was slow thanks to her weight-gain and her comrades weren’t marathon participants either. “Boy, I’m really tired from all of this…how much farther do we have to go? It looks like we’re still quite a ways away from the ship. I really wished we had that expensive donkey.”

Pedro then felt something hard hit his head. He turned around and saw Petriva, the MOLE RAT, throwing rocks at Kuro and himself. Darn! She didn't fail calculus did she, now Hopra has someone who can hit me with cannons...and rocks.

Kuro wasn't so thrilled about this discovery. He had a special dislike for rocks coming at him at great speeds. He jumped on Pedro's shoulders, petrified. "Go Pedro, sir! GO!!!"

More and more rocks were coming at them. Petriva had a good arm. Pedro started to run but Kuro's paws were blocking his vision, so his straight path towards the ship was no longer... straight.

To Be Continued…

Problem: Queen Hopra chases Pedro and Kuro for five seconds. The two pandas' velocity is given by 3t^tcos(t) metres per second. What is he total distance the pandas travelled after five seconds? Did they get to the ship safely?

Solution:http://pandasolutions-apcalc06.blogspot.com/2007/02/solution-part-3.html