Fig. P4.65, p.108

Active Figure 4.7  The parabolic path of a projectile that leaves the origin with a velocity vi. The velocity vector v changes with time in both magnitude and direction. This change is the result of acceleration in the negative y direction. The x component of velocity remains constant in time because there is no acceleration along the horizontal direction. The y component of velocity is zero at the peak of the path. At the Active Figures link at http://www.pse6.com you can change launch angle and initial speed. You can also observe the changing components of velocity along the trajectory of the projectile. Fig. 4.7, p.84

Figure 4.9  Motion diagram for a projectile. Fig. 4.9, p.85

Figure 4.13 (a) Multiflash photograph of projectile-target demonstration. If the gun is aimed directly at the target and is fired at the same instant the target begins to fall, the projectile will hit the target. Fig. 4.13a, p.88

Figure 4.13 (b) Schematic diagram of the projectile-target demonstration. Both projectile and target have fallen through the same vertical distance at time t, because both experience the same acceleration ay = –g. Fig. 4.13b, p.88

Figure 4.15 A package of emergency supplies is dropped from a plane to stranded explorers. Fig. 4.15, p.90

Figure 4.1  A particle moving in the xy plane is located with the position vector r drawn from the origin to the particle. The displacement of the particle as it moves from A to B in the time interval ∆t = tf – ti is equal to the vector ∆r = rf – ri. Fig. 4.1, p.78

Figure 4.3  As a particle moves between two points, its average velocity is in the direction of the displacement vector ∆r. As the end point of the path is moved from B to B’ to B’’, the respective displacements and corresponding time intervals become smaller and smaller. In the limit that the end point approaches A, ∆t approaches zero, and the direction of ∆r approaches that of the line tangent to the curve at A. By definition, the instantaneous velocity at A is directed along this tangent line. Fig. 4.3, p.78

Figure 4. 4 A particle moves from position A to position B Figure 4.4  A particle moves from position A to position B. Its velocity vector changes from vi to vf. The vector diagrams at the upper right show two ways of determining the vector ∆v from the initial and final velocities. Fig. 4.4, p.80

Figure 4.17  (a) A car moving along a circular path at constant speed experiences uniform circular motion. (b) As a particle moves from A to B, its velocity vector changes from vi to vf. (c) The construction for determining the direction of the change in velocity ∆v, which is toward the center of the circle for small ∆r. Fig. 4.17, p.92

Figure 4.17  (a) A car moving along a circular path at constant speed experiences uniform circular motion. Fig. 4.17a, p.92

Figure 4.17   (b) As a particle moves from A to B, its velocity vector changes from vi to vf. Fig. 4.17b, p.92

Figure 4.17   (c) The construction for determining the direction of the change in velocity ∆v, which is toward the center of the circle for small ∆r. Fig. 4.17c, p.92

Figure 4.19   (b) The total acceleration a of a particle moving along a curved path (which at any instant is part of a circle of radius r) is the sum of radial and tangential components. The radial component is directed toward the center of curvature. If the tangential component of acceleration becomes zero, the particle follows uniform circular motion. Fig. 4.19b, p.95

Fig. P4.47a, p.106

Fig. P4.53, p.106

Figure 4.24 A boat aims directly across a river and ends up downstream. Fig. 4.24, p.98

Figure 4.25 To move directly across the river, the boat must aim upstream. Fig. 4.25, p.99