(these are my quick notes from Day 3 of presentations)
Python and Calculus
Described the python, vpython, sympy programming languages/libraries. Next they are showing how they used python and the sympy libraries to calculate the derivative of a given function. It graphs the function and asks where they want to draw the tangent line.
They were trying to make a parachute that fell the slowest. They changed the diameters of the parachutes, and the wire placement. They also varied the amount of weight on the parachute. Used tracker analysis to see position, velocity, and acceleration. Showed the tracker info to find the velocity of the parachute. Used a t=1 to compare the speeds of all the parachutes. The “best” parachute has the least velocity. Conclusion – bigger parachutes with cross wires worked the best.
How to count cards and betting strategy
Explained the rules of Blackjack. Went through basic strategy, and then went through how to count cards. Cards 2-6 add 1, 10 and face subtract 1. If the count is positive, then you are more likely to get a high card. If you can count cards, you can win around 52% of the time instead of 49% of the time. If you have a high count, then you increase your betting amount because you are more likely to win. Flat betting is betting the same amount of money each hand. Martingale betting system has the person double their previous losing bet. Cancellation Betting system is where you write down a series of numbers, you bet the sum of the first and last numbers etc. Mimic the Dealer is a bad gambling strategy. Never Bust is where the house has a advantage of 4%. Assume ten in the hole gives the house 10% advantage. Walked through the python program and showed the simulations
Relationship between calculus, projectile motion and discus
(lost the description – darn you google docs)
Showed the blacklight pendulum wave machine. Each string is a different length so they have a different period. The longest pendulum has 45 oscillations in 60 sec, 46 oscillations in 60 sec, 47 oscillations in 60 sec. etc. You can choose what period you want by using a formula that will find the pendulum length. Did a full demo and then showed their full video. Used desmos to show the sine waves for the 5 different masses.
Researched how to create string art. String art uses tangent lines to create a curve. String art can create all differentiable functions. (unfortunately her presentation was rushed due to the lack of time in the block).
Baking Soda and Vinegar Rockets
Launched the rockets at 45 degree angle to get the maximum distance. Measured the distances of the rockets. They found the ratio 12g vinegar to 1g baking soda to maximize the distance of the rocket. Went over the horizontal distance equation and how you could use the time of flight to find the distance of the rocket (or vice versa).