12 Projectile Vectors Student
LivePhoto Physics Activity 12 Name: __________________________ 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 <Galileo's Projectile_15fps.mov> and review the definitions of two-dimensional displacement and velocity vectors. 1. Preliminary Questions
(a) Suppose an object is moving in a plane and we choose to describe it using an x-y coordinate system. If the object is at location x1, y1 at time t1 and at location x2, y2 at time t2, then it has been “displaced.” The mathematical definition of its displacement vector is
2 1 ˆ i +(y2 − y1)ˆ j Δr =Δx +Δy = (x − x )
where Δx and Δy are the x and y-components of the object’s displacement in the time period. A displacement vector Δr is shown in the diagram below. Draw and label the x-component of the displacement vector (denote it as Δx ) of the vector Δr . Place the tail of the vector at x1, y1. Hint: This vector component points in the x-direction only. x1,y1
x2,y2
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 <Galileo's Projectile_15fps.mov> and review the definitions of two-dimensional displacement and velocity vectors. 1. Preliminary Questions
(a) Suppose an object is moving in a plane and we choose to describe it using an x-y coordinate system. If the object is at location x1, y1 at time t1 and at location x2, y2 at time t2, then it has been “displaced.” The mathematical definition of its displacement vector is
2 1 ˆ i +(y2 − y1)ˆ j Δr =Δx +Δy = (x − x )
where Δx and Δy are the x and y-components of the object’s displacement in the time period. A displacement vector Δr is shown in the diagram below. Draw and label the x-component of the displacement vector (denote it as Δx ) of the vector Δr . Place the tail of the vector at x1, y1. Hint: This vector component points in the x-direction only. x1,y1
x2,y2