![]() ![]() Physics tells us that the horizontal motion of the projectile is linear that is, the horizontal speed of the projectile is constant. In this section, well discuss parametric equations and some common applications, such as projectile motion problems. For many of these scenarios, it is easier and much more useful to have the. Particularly when the we encounter motion for which the location is a function of time. ![]() (Thus \(h(0) = h(192) = 0\)ft.) Find parametric equations \(x=f(t)\), \(y=g(t)\) for the path of the projectile where \(x\) is the horizontal distance the object has traveled at time \(t\) (in seconds) and \(y\) is the height at time \(t\). However, when it comes time to use our mathematical toolbox on real applied problems, parametric equations naturally arise. Assuming ideal projectile motion, the height, in feet, of the object can be described by \(h(x) = -x^2/64+3x\), where \(x\) is the distance in feet from the initial location. Sometimes the trajectory of a moving object is better stated as a set of parametric equations like x(t) & y(t) than as a traditional function like. of curve (but this equation doesn’t contain any time information so we still have to go back to the parametric equations to plot some points and indicate direction). \): Converting from rectangular to parametricĪn object is fired from a height of 0ft and lands 6 seconds later, 192ft away.
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