Sunday, May 4, 2014

Parabolas

I was thinking about parabolas and when I see them or use them in daily life. It struck me, as I was thinking about the upcoming state tennis tournament, that I see a parabola every time I toss a ball to serve. (That's a lot of parabolas.) Here is what my toss would look like if I graphed it:
I toss the tennis ball about four feet in the air, so the maximum y value would be at 4 on the graph. If we were to graph the height of the toss vs time, the y-axis would be height (h) and the x-axis would be time (t). Assume I released the ball at about nine feet in the air. One x intercept would be at the origin. This makes sense, because at 0 seconds, the ball hasn't gone anywhere.Let's assume that the ball travels up at about 40 ft/second and the velocity coming back down changed by 16 ft/s every second (so v= 16 ft/s^2). So the height for the parabola would be calculated using the equation:
h = -16t^2 + 40 t - 9

with help from http://www.mathsisfun.com/algebra/quadratic-equation-real-world.html


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