• You have 5 cities to protect. Three get destroyed, and half of your remaining cities also explode. How many cities do you have at the end of the level? 

• You want to know how many missiles you have in your right silo. The sum of the three silo’s ammunition is 42. The middle silo has the least ammunition, and the left silo has two more. All the ammunition amounts are consecutive even numbers. 

• One missile enters the screen 4 seconds before another faster missile going straight down. One missile travels half the speed of the other, and the sum of the two velocities is 1.65 pixels per second. Given they had the same trajectory and starting location, how many seconds after the first missile enters the screen will they be in the exact same place so that you can hit them both perfectly at the same time? 

• You’ve won level 3! Before this level your score was 382. For each city remaining you gain 50 points, and you have finished the level with five cities undestroyed. You get 5 points for every unused missile, and there are 30 unused missiles. How many cities do you need to have minimum at the end of your next level to win that level and reach 800 points? 

• You’ve enjoyed this game at the arcade for a while now, but it’s 1981 and you only have a game boy, not an Atari 2600 (being that you’re a time traveler). If developers, hypothetically, start porting to the game boy right as you think this thought and progress at a rate of 14.28571429% per year for the first half of completing development but are only a third as fast for the second half, how many years will it take for them to finish so you can time travel forward to that year?

• You were so distracted by thinking about your anachronistic-game-boy-hypothetical that your leftmost city was destroyed by a missile. At the beginning of the game, it had a hypothetical population of 189,216,000 people and an average hypothetical birth rate of 5% per year. So far, your game lasted 30 seconds. About how many hypothetical individuals in this city lived and died their entire lives in the span of your game? 

• A missile gets dropped from rest 700 pixels directly above your city. The missile accelerates straight downward with an acceleration of 10 pixels per second squared. In response, you fire a counter missile with a velocity of 2 pixels per second which flies only horizontally with constant velocity. Your counter missile collides with the enemy missile 200 pixels above your city. How many pixels did your counter missile have to travel?

• Your missiles explode with a radius of 15 pixels. The missiles on the screen enter all at the same time and with the same vertical velocity. They are as follows:

  1. 1.  One missile starts 30.9 pixels into the screen at an angle of 39.4 from the top of the screen leaning to the left. 

     2. Another missile starts 23.5 pixels into the screen at an angle of 78.3 from the top of the screen leaning to the right. 

     3. A third missile starts 33.4 pixels into the screen at an angle of 84 from the top of the screen leaning to the left. 

     4. A fourth missile starts 0 pixels into the screen at an angle of 86.9 from the top of the screen leaning to the right. 

     5. A fifth missile starts 38.5 pixels into the screen at an angle of 85 from the top of the screen to the left. 

     6. A sixth missile starts 10.8 pixels into the screen at an angle of 48 from the top of the screen leaning to the right. 

     7. A seventh missile starts 38.5 pixels into the screen at an angle of 38 from the top of the screen leaning to the left. 

     8. An eighth starts 15.2 pixels into the screen at an angle of 63.1 from the top of the screen leaning to the right. 

     9. A ninth missile starts 23 pixels into the screen at an angle of 88.4 from the top of the screen leaning to the left. 

     10. The last missile starts 30.2 pixels into the screen at an angle of 78.4 from the top of the screen leaning to the left. 

If you make the best shot physically possible within 16 pixels of the top of the screen and get as many enemy  missiles in one radius of your blast as you can, how many enemy missiles do you stop? 

• The acceleration vector of a missile at a time t with initial velocity and acceleration vector valued function defined below. How far from its initial position is the missile after 3 seconds?