A Classical Approach of Newtonian Mechanics

2 MOTION IN 1 DIMENSION 2.7 Free-fall under gravity 0 The quantity v 0 is determined from the graph as the intercept of the stra ...

2 MOTION IN 1 DIMENSION 2.7 Free-fall under gravity 0 g x 0 A B C t D Figure 9: Graph of displacement versus time Equations (2.1 ...

2 MOTION IN 1 DIMENSION 2.7 Free-fall under gravity Suppose that a ball is thrown vertically upwards from ground level with velo ...

2 MOTION IN 1 DIMENSION 2.7 Free-fall under gravity ∫ × Question: Consider the motion of the object whose velocity-time graph is ...

2 MOTION IN 1 DIMENSION 2.7 Free-fall under gravity s Worked example 2.2: Speed trap Question: In a speed trap, two pressure-act ...

2 MOTION IN 1 DIMENSION 2.7 Free-fall under gravity = −2.73 m s−^2. ...

3 MOTION IN 3 DIMENSIONS 2.Motion in 3 dimensions 1.14 Introduction The purpose of this section is to generalize the previously ...

3 MOTION IN 3 DIMENSIONS 3.3 Vector displacement R O Figure 11: A vector displacement 1.16 Vector displacement Consider the moti ...

3 MOTION IN 3 DIMENSIONS 3.4 Vector addition R O Figure 12: Vector addition z-axes), finally move z meters along the z-axis (per ...

3 MOTION IN 3 DIMENSIONS 3.5 Vector magnitude Suppose that the components of vectors r 1 and r 2 are (x 1 , y 1 , z 1 ) and (x 2 ...

3 MOTION IN 3 DIMENSIONS 3.7 Diagonals of a parallelogram C A Figure 13: A parallelogram that of the latter. Note that if λ is n ...

3 MOTION IN 3 DIMENSIONS 3.8 Vector velocity and vector acceleration centroid X from point A can be written in one of two differ ...

3 MOTION IN 3 DIMENSIONS 3.8 Vector velocity and vector acceleration By analogy with the 1 - dimensional equation (2.3), the bod ...

3 MOTION IN 3 DIMENSIONS 3.9 Motion with constant velocity The corresponding components of the body’s velocity are then simply d ...

3 MOTION IN 3 DIMENSIONS 3.10 Motion with constant acceleration 0 · Figure 14: Motion with constant velocity Hence, the object’s ...

3 MOTION IN 3 DIMENSIONS 3.11 Projectile motion s |s| (^) a. s = |a| |s| cos     a |a| |s| cos  Figure 15: The scalar pr ...

3 MOTION IN 3 DIMENSIONS 3.11 Projectile motion z x v 0 cos   Figure 16: Coordinates for the projectile problem Our first tas ...

3 MOTION IN 3 DIMENSIONS 3.11 Projectile motion (^0 0) s = (x, y, z) from its launch point satisfies [see Eq. (3.35)] s = v 0 t ...

3 MOTION IN 3 DIMENSIONS 3.12 Relative velocity 0 z x R Figure 17: The parabolic trajectory of a projectile Note that the range ...

3 MOTION IN 3 DIMENSIONS 3.12 Relative velocity (^) Figure 18: Relative velocity to the ground. What is the vector velocity vg o ...