__PLEASE WAIT PATIENTLY UNTIL THE NEXT QUESTION OF THE DAY ON JANUARY 2ND. THANKS.__

Heyo everyone!

Here is the next checkpoint everyone! Everyone can work on these questions together - and points will be distributed out! This is another checkpoint because the last one was very inactive. Let's see how active this one will be!

This blog post will be removed after the checkpoint is completed on September 10th. But you must SHOW YOUR WORK to get full credit.

ANY QUESTIONS ON THE LAST CHECKPOINT? FEEL FREE TO ASK, AND I WILL TRY TO WORK IT OUT.

## Questions

And good luck! These questions are supposed to be hard, so don't worry if you don't get them. There is no penalty for guessing on these questions.

1. (PLEASE ASSUME G=10M/S^{2} FOR ALL PROLEMS, AND TREAT AIR RESISTANCE AS NEGLIGIBLE). United in their hatred of 3primetime3, Kool Saif Mohd and Variousthings3251 plot revenge. They drug his coffee, tie up their slumbering victim, and load him into a giant cannon meant for launching circus clowns. The cannon is erected atop 3primetime3's cousin's apartment, 12 meters off the ground, and upon regaining awareness, the user is fired out of the cannon in the general direction of 3primetime3's house. He is launched at an angle of 36.9 degrees above the horizontal, with an initial velocity of 50m/s.

1a) How high off the ground is the top of 3primetime3's trajectory?

1b) When 3primetime3 is just about to hit the ground, in what direction is he traveling with respect to the horizontal?

1c) Fortunately for 3primetime3, he is good friends with Batman. Just as he is about to hit the ground, Batman wizzes by in his Batmobile, careening through the world along 3primetime3's line of flight directly toward the cannon at 40 m/s. 3primetime3 lands neatly in the passenger seat, and through magic, is entirely uninjured. In Batman's reference frame, at what speed was 3primetime3 initially launched?

1d) What is the equation for 3primetime3's speed in the ground frame (this is different from velocity!) as a function of time while he is in the air?

2. 3primetime3 gets dropped off at a near amusement park, takes a break and was about to go home. Just then, a little nice ride called the "Merry-Go-Round" caught his eye, and he went to take a ride. This seemingly harmless merry-go-round has a radius of 6 meters, and it is supposed to rotate at a nice gentle constant rate of 2.00 revolutions per minute. Yet danger lurks menacingly later in the problem.

2a) What is the magnitude of the centripetal acceleration in m/s^{2} during ordinary operation?

2b) The motor controller has gone wild! With reckless abandon, the merry-go-round spins faster and faster! It's rate of revolution begins to increase precipitously, with a constant tangential acceleration of 2m/s^{2}. 3primetime3 clings desperately to the giant fiberglass poodle upon which he has been seated, his safety belt now dangerously unfastened. Oh no! How fast is 3primetime3 moving 3 seconds after the motor controller fails?

2c) What is the magnitude of 3primetime3's centripetal acceleration 3 seconds after the motor controller fails?

3primetime3's grip is only strong enough to sustain 0.8g of total horizontal acceleration before he slides loose from his slippery perch. Batman, who was still around, catches 3primetime3 again and brings him back to his house safely (before 3primetime3 can find any more distractions to get injured). 3primetime3 thanks Batman for saving his life twice and records the moment on Prime Numbers Wiki Checkpoint 5 to remember for the rest of his life.

## Leaderboards

1. Blueeighthnote: 13843 points (2 achvmt pkgs) - One more to get the next lucky prime badge!

2. Minipop56: 12206 points - Four more to get the next lucky prime badge!

3. TimBluesWin: 755 points (1 achvmt pkg)

4. Imamadmad: 745 points (1 achvmt pkg)

5. Julianthewiki: 525 points (1 achvmt pkg) - RETIRED

6. Dalek-James: 380 points

7. Wikia Contributor 69.235...: 230 points (1 achvmt pkg)

8. Lefty7788: 300 points - One more to get the next lucky prime badge!

9. Supermario3459: 145 points (1 achvmt pkg)

10. ZombieBird4000: 50 points (1 achvmt pkg)

11. Wildoneshelper: 40 points (1 achvmt pkg)

12. Emmaelise401: 50 points

13. CalzoneManiac: 30 points

14. 21qmcgagin: 20 points

15. Kyodaisuu: 21 points

16. Googleaarex: 10 points

## Achievements

### Skillz Badges!

Usually awarded for having skills to solving hard questions, etc.

1. Quick Thinker! (+10 points) - Awarded for posting an answer before I write "Please leave your answers here." FIRST FOUNDED BY BLUEEIGHTHNOTE

2. RARE: Leaderboards Expert! (+300 points) - Awarded for being 1st place on the leaderboards for 30+ days. FIRST FOUNDED BY BLUEEIGHTHNOTE

3. RARE: More than a Millenium! (+100 points) - Awarded for being first in the leaderboards and scoring more than 1000 points from the runner-up. FIRST FOUNDED BY BLUEEIGHTHNOTE

4. Questions in a question (+20 points)? Awarded for finding three ambiguities in a single question. EARNED BY IMAMADMAD

### Earth Badges

Most rare ones are found here.

1. RARE: Top Ten (+30 points) - Awarded for being the first top 10 people ONLY to participate on the question of the day! EARNED BY THE FIRST 10 PARTICIPATING PEOPLE

2. RARE: Cyclone Centurion! (+250 points) - Awarded for scoring at least 10000 points in the QOTD system! FIRST FOUNDED BY BLUEEIGHTHNOTE.

### Sun Badges

All epic ones are found here.

1. EPIC: Lucky Primer (+100 points): Congratulations! You have guessed the lucky prime correctly. Get the Lucky Prime two more times to earn the next achievement! FIRST FOUNDED BY JULIANTHEWIKI.

2. EPIC: Very Lucky Primer (+200 points): Congratulations! You have guessed the lucky prime correctly two more times. Get the Lucky Prime three more times to earn the next achievement! FIRST FOUNDED BY MINIPOP56 AND BLUEEIGHTHNOTE.

3. REALLLLY LUCKY PRIMER (+300 points): Congratulations! You have guessed the lucky prime correctly three more times. Get the Lucky Prime four more times to earn the next achievement! FIRST FOUNDED BY MINIPOP56.

### Galaxy Badges

Mysterious badges from a far-out universe. Each one found here is worth 10000+ points and/or 5+ achievement packages.

1. MYSTERY: ATLAS (+10000 points) - ??? FIRST FOUNDED BY BLUEEIGHTHNOTE.

### Uniqueness Badges

Unique things one can do in the answers section. ONLY ONE PERSON CAN EARN EACH BADGE.

1. Analyzer! (+10 points) - Awarded for drawing a diagram. FOUNDED BY IMAMADMAD

2. Inspiration! (+5 points) - A question was dedicated to you! FOUNDED BY BLUEEIGHTHNOTE

### Trustworthiness Badges

Awarded by how much I trust someone on this wiki. Please do not ask me about these badges.

1. Reliability (+100 points) - Trusted to write a question of a day. FIRST FOUNDED BY BLUEEIGHTHNOTE, AND IMAMADMAD

2. Scoreboard Tinkerer (+100 points) - Trusted to change the scoreboards. FIRST FOUNDED BY BLUEEIGHTHNOTE AND JULIANTHEWIKI

3. Prime Staff (+100 points) - Become a chat moderator, rollbacker, sysop, or bureaucrat on this wikia! FIRST FOUNDED BY BLUEEIGHTHNOTE, JULIANTHEWIKI, TIMBLUESWIN, IMAMADMAD, SUPERMARIO3459, MINIPOP56, AND DALEK-JAMES

### Duration Badges

Yes! YOU KNOW IT! PARTICIPATION EVERY DAY!

1. 4-Leaf Clover! (+100 points) - Awarded for participating on the Question of the Day everyday during the month of March! FIRST FOUNDED BY MINIPOP56.

2. April Fools! (+100 points) - Awarded for participating on the Question of the Day everyday during the month of April! FIRST FOUNDED BY MINIPOP56.