2020 issue 6

Judge’s Choice Lina Paola Espejo Ramirez Midland College Math in the Picture Contest Winners 2019 People’s Choice Kassidy Kotulan Texas State University Texas State University Department of Mathematics 601 University Drive San Marcos, Texas 78666-4684 The math rippling on top of the San Marcos River is a brilliant method to learning where you live. The vibration frequency of the San Marcos Salamander coming to the surface of the water causes a wave to disperse in a trigonometric wave function. To understand the math of our ripple, we need to know the area inside of the ripple at time t , to then find the rate at which the area is increasing. We can find the solution to the area of our ripple by (a) and the rate of change at which the area of our ripple increases at time t by (b) Using equation (b) you can find the rate of change of any ripple you create! To find the size of the force due to spin use this equation: ||Fs|| = Ksω||v|| where ω is angular velocity and Ks is the proportionality constant for spin. The serve in a volleyball match is considered the first attack action in a game. The primary goal of an effective serve is to give the receivers the least amount of time possible to react. There are many types of serve but I will focus in the top-spin serve. The spin on the ball produces a force that acts perpendicular to the velocity of the ball. The top of the ball is spinning in the same direction as the ball’s motion. The ball is moving through individual air molecules as it spins. On the top of the ball, the air molecules are being pulled forward by the spinning ball. However, the air is also being pushed backward as the ball moves. Thus, air molecules at the top of the ball and are moving faster than the ones in the bottom of the ball. The air molecules are accumulating on the top of the ball while in the bottom the spin of the ball compensates for the movement of the ball, pushing the air molecules backward off the ball so there is no accumulation. This difference in accumulation of air molecules creates a higher pressure on top of the ball. So, a ball moving through the air with top-spin, will experience a downward force due to the spin, which makes the ball drop to the ground faster than it would with no spin. Picture from Midland College volleyball team (Lina Espejo) by Forest Allen