Kinematics in Two Dimensions Chapter 3 Kinematics in Two Dimensions

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

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

Velocity Average velocity Instantaneous velocity

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

Acceleration Average acceleration Instantaneous acceleration

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

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

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

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

Projectile motion: putting X and Y together

Projectile motion: trajectory and range

Projectile motion: trajectory and range

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.

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

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

Questions?