![]() Projectile Motion at a Height: Projectile motion of an object with initial height y 0, initial. What is an alternative way of solving for time in this situation?ġ0 10.7 HW Assignment Pg. Often, parametric equations are used to describe the motion of an object over time. How far does the ball travel?ħ Example 3: To find when the ball hits the ground, we set the second equation equal to zero and solveĨ What is an alternative way of solving for time in this situation?Įxample 3: Since the problem only makes sense if we time starting from t=0 we’ll use the second value in our horizontal distance equation. A sketch of the parametric curve (including direction of motion) based on the equation you get by eliminating the parameter. (c) The velocity in the vertical direction begins to decrease as the object rises. (b) The horizontal motion is simple, because a x 0 a x 0 and v x v x is a constant. Study additional parametric equation problems, such as those on the Parametric Equations Problem Sampler. Figure 4.12 (a) We analyze two-dimensional projectile motion by breaking it into two independent one-dimensional motions along the vertical and horizontal axes. By choosing a convenient orientation of our coordinate system we have simplified the mathematics involved in solving a projectile motion problem. ![]() ![]() Copy the related handout for students to. With the appropriate orientation of coordinate axes we can can treat projectile motion as motion in two dimensions with v x v 0x, x x 0 + v 0x t, v y v 0y + a y t, y y 0 + v 0y t + at 2. Load the humancannons.tns file onto all student calculators. If v is the velocity vector with angle θ, then the horizontal and vertical components can be found by the following equations:Ħ Example 3: Jack throws a baseball from 6 ft above the ground with an initial speed of 20 ft/sec at an angle of 35°. Interpreting Graphs of Quadratic Equations. 1 10.7 Parametric Equations parametric equations: a pair of equations, one for x and one for y, relating both to a third variable t.Ģ Example 1: Eliminate the parameter for the curve below:ģ Example 2: Eliminate the parameter for the curve below:Ĥ Projectile Motion When a projectile is in two dimensional motion, the parametric equations for its motion are defined as follows: Parametric equations are also very useful for projectile motion applications. Find parametric equations and a parameter interval for the motion of a particle that starts at (0, -a) and traces the circle x² + y² a² a.
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