Use the information below to generate a citation. Then you must include on every digital page view the following attribution: Projectile Motion (with Parametric Equations) Math Lib ActivityStudents will practice solving projectile motion problems using parametric equations with this Math Lib Activity. If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Changes were made to the original material, including updates to art, structure, and other content updates. Want to cite, share, or modify this book? This book uses theĪnd you must attribute Texas Education Agency (TEA). To do this, we separate projectile motion into the two components of its motion, one along the horizontal axis and the other along the vertical. Since vertical and horizontal motions are independent, we can analyze them separately, along perpendicular axes. Keep in mind that if the cannon launched the ball with any vertical component to the velocity, the vertical displacements would not line up perfectly. You can see that the cannonball in free fall falls at the same rate as the cannonball in projectile motion. Figure 5.27 compares a cannonball in free fall (in blue) to a cannonball launched horizontally in projectile motion (in red). The most important concept in projectile motion is that when air resistance is ignored, horizontal and vertical motions are independent, meaning that they don’t influence one another. Write an equation describing the height at seconds. Ask students to guess what the motion of a projectile might depend on? Is the initial velocity important? Is the angle important? How will these things affect its height and the distance it covers? Introduce the concept of air resistance. Suppose a soccer ball is kicked upward from a height of 6 feet at an initial velocity of 48 ft/sec. Or to Mars or Neptune since their gravities are friendlier to factor.Review addition of vectors graphically and analytically. If you’re at your wits end looking for different numbers – other than -16 – to use with quadratic equations in projectile motion, try sending the problem to the Moon. If you need metric/SI units, here’s a table for accelerations due to gravity in meters per second per second. If you’re using customary units, here are different accelerations due to gravity in feet per second per second. Using the ratios from NASA, you can generate the following list of values for other planets’ accelerations due to gravity. In projectile motion, the general form of the quadratic function of height as a function of time is h( t) =, where g represents the acceleration due to gravity, represents the initial velocity, and represents the object’s initial height. If you’re using customary units of measure, the acceleration due to gravity on Earth is about 32 feet per second per second (ft/sec2). NASA has a spiffy planetary fact sheet that compares attributes of other planets (and Pluto, which is an ex-planet - is there a support group for planets that got kicked out of the club?) to Earth using ratios. Interplanetary Road Trip with Quadratic Equations!įortunately, there are plenty of other places in the solar system to obtain different coefficients for quadratic functions rooted in projectile motion. Coefficients of -16 and -4.9 are directly related to Earth’s gravity, so it’s hard to change those values so that the curve makes a prettier graph or so that the equation becomes more easily factorable. Projectile motion is a great context and is highly relevant both to students and to a variety of careers and situations. –Disgruntled Curriculum Specialist, Could Be Your ISDĮver feel like every quadratic equation has an x-squared term with a coefficient of -16 or -4.9? -16 factors nicely but -4.9 certainly doesn’t. No, dear, you cannot change -16 to -12 in the quadratic equation because it factors more nicely.
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