Understanding Projectile Motion in Two Dimensions

1. Chapter 3 Kinematics in Two Dimensions

2. Position The position of an object is described by its position vector,

3. Displacement The displacement of the object is defined as the change in its position,

4. Velocity • Average velocity • Instantaneous velocity

5. Instantaneous velocity Vector of instantaneous velocity is always tangential to the object’s path at the object’s position

6. Acceleration • Average acceleration • Instantaneous acceleration

7. Acceleration • Acceleration – the rate of change of velocity (vector) • The magnitude of the velocity (the speed) can change – tangential acceleration • The direction of the velocity can change – radial acceleration • Both the magnitude and the direction can change

8. Projectile motion • A special case of 2D motion • An object moves in the presence of Earth’s gravity • We neglect the air friction and the rotation of the Earth • As a result, the object moves in a vertical plane and follows a parabolic path • The x and y directions of motion are treated independently

9. Projectile motion – X direction • A uniform motion: ax = 0 • Initial velocity is • Displacement in the x direction is described as

10. Projectile motion – Y direction • Motion with a constant acceleration: ay = – g • Initial velocity is • Therefore • Displacement in the y direction is described as

11. Projectile motion: putting X and Y together

12. Projectile motion: trajectoryand range

13. Projectile motion: trajectoryand range

14. Chapter 3 Problem 47 The drawing shows an exaggerated view of a rifle that has been “sighted in” for a 91.4-meter target. If the muzzle speed of the bullet is v0 = 427 m/s, what are the two possible angles q1 and q2 between the rifle barrel and the horizontal such that the bullet will hit the target? One of these angles is so large that it is never used in target shooting.

15. Relative motion • Reference frame: physical object and a coordinate system attached to it • Reference frames can move relative to each other • We can measure displacements, velocities, accelerations, etc. separately in different reference frames

16. Relative motion • If reference frames A and B move relative to each other with a constant velocity • Then • Acceleration measured in both reference frames will be the same

17. Questions?