Chapter 4 Sections 1-3 Motion along x axis is independent of motion along y axis. This fact is a result of the properties of vectors and Newton’s laws (coming soon). Motion between the x and y axes is connected by the time variable, t. MAIN CONCEPTS

Figure 4-1b Constant Velocity NEW NOTATION: subscripts for “x” and “y” axes

Example 4-1 The Eagle Descends Motion in x and y directions is treated independently.

Figure 4-3 Independence of Vertical and Horizontal Motions X-motion Y-motion

Figure 4-2 Acceleration in Free Fall

Table 4-1 Constant-Acceleration Equations of Motion x = x 0 + v 0x t + ½ a x t 2 v x = v 0x + a x t v x 2 = v 0x 2 + 2a x  x y = y 0 + v 0y t + ½ a y t 2 v y = v 0y + a y t v y 2 = v 0y 2 + 2a y  x Position as a function of time Velocity as a function of time Velocity as a function of position NOTE: The equations are the same, except for the subscript which identifies the axis of motion.

Concept Quick Quiz: How do the splashdown speeds compare? Diver 1 drops straight down. Diver 2 jumps horizontally with speed v_o.

How do the TOTAL SPEEDS of the two divers compare? 1. Diver 1 (straight down) is higher. 2. Diver 2 (straight out) is higher. 3. They are the same.

Physlets I3.4 showing the independence of x and y motions

Spreadsheet Physics for Ballistic Motion: Cannonball problem

Physlets Exploration 3.5, illustrating projectile motion

Conceptual Quick Quiz How do the landing speeds compare? Ball 1 thrown upwards. Ball 2 thrown downwards. Magnitude of angle is the same.