# 12 Projectile Vectors Student

Date: __________________10/22/14_________ Projectile Motion Vectors There are multiple ways to represent an object’s motion. If the motion is two-dimensional and lies in a plane, some representations include: (1) recording x and y coordinates of the object at different times in a data table; (2) displaying the object’s x and y locations at regular time intervals on a diagram; (3) drawing vectors showing displacement, velocity, and acceleration and their x and y components at different times. (4) using vector equations to represent velocity and acceleration vectors quantitatively. In this activity you will practice representing the motion shown in Figure 1 using vectors and vector equations that represent displacements as well as average velocities and accelerations in the 1/15th of a second time intervals between position measurements. Figure 1: A motion diagram showing a ball’s locations every 1/15ths as it rolls horizontally and then falls vertically for about 1 meter. Before working on this activity, you should view the movie entitled Physics with Video Analysis 12 - 1

(b) Once again the displacement vector Δr is shown in the diagram below. Draw and label the ycomponent of the displacement vector (denote it as Δy ) of the vector Δr . Place the tail of the vector at x1, y1. Hints: This component points in the y-direction only and the length of Δy is less than the length of Δx . x1,y1

x2,y2

(c) The vector equation that defines average velocity during a time interval Δt = t2 − t1 is v → =Δr = (x2 − x1) ˆ i + (y2 − y1) ˆ j . 1 2

Δt(t2 −t1)(t2 −t1)

Explain why the relative lengths of the displacement-vector components you drew in parts (a) and (b) should be proportional to the lengths of the corresponding velocity vector components. They are all over the same number, which is the change in time. (d) The motion diagram in Figure 1 is a composite diagram constructed from a video analysis of the movie . The movie has been scaled in meters. If you view the movie on a frame-by-frame basis for all 11 frames, you will see that video analysis has already been used to determine the location of the ball in each frame. Figures 2 and 3 depict the location of the falling ball in...

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