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Modules Open College - e-Learning Content Library
Parabolic trajectory

A graph of function f(x) = ax2+bx+c if a is not equal to zero is called a parabola. A trajectory of a missile is an example of a parabola. Consider a missile start from the point of origin with velocity V and an angle of departure α. The horizontal and vertical part of motion for the missile is described by set of equations x(t) = tV cos α and y(t) = tV sin α - g t2. Thus y(x) = x∙tg α + x2g/(V2 cos2 α). This is a quadratic function with a = g/(V2 cos2 α), b = tg α and c = 0. Cross points of its graph with axis OX are the point of origin and a point (0; L) where L = (V2∙sin 2α) / g is a shot distance.

The model has 2 modes: a Demonstration and a Find distance.

In Demonstration mode you can set the initial speed and the angle. Corresponding shot distance calculates automatically. The Start button draw a graph of the given function (the missile trajectory) and allows you to observe the missile flying. A Next button allow you to set a different initial data.

In Find distance mode you should find a shot distance for given values of V and α. Enter the solution to place the refuse bin correctly. Press the Check button to observe shooting. Press the Show solution button to see a correct solution.

© OpenTeach Software, 2007