chapter 4 sections 1-3 motion along x axis is independent of motion along y axis. this fact is a...
DESCRIPTION
Example 4-1 The Eagle Descends Motion in x and y directions is treated independently.TRANSCRIPT
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 4-1bConstant Velocity
NEW NOTATION: subscripts for “x” and “y” axes
Example 4-1The Eagle Descends
Motion in x and y directions is treated independently.
h
hvvx
tvhtvx
y
x
y
x
tan0
0
0
0
Figure 4-3Independence of Vertical and Horizontal Motions
X-motion Y-motion
x
x
vvtvx
0
0
gtvv
gttvyy
y
y
0
200 2
1
Figure 4-2Acceleration in Free Fall
Table 4-1Constant-Acceleration Equations of Motion
x = x0 + v0xt + ½ axt2 vx = v0x + axt vx2 = v0x2 + 2axx
y = y0 + v0yt + ½ ayt2 vy = v0y + ayt vy2 = v0y2 + 2ayx
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.
0% 0% 0%
1 2 3
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
Simulation of two dimensional motion in gravity.
dt 0.014 g 9.800v_0 10.000theta, deg. 45.000 theta 0.785 radians
Time X_pos X_vel Y_pos Y_vel0.000 0.000 7.071 0.000 7.0710.014 0.099 7.071 0.099 6.9340.028 0.198 7.071 0.196 6.7970.042 0.297 7.071 0.291 6.6590.056 0.396 7.071 0.384 6.522
Y Position vs. Time
0.000
0.500
1.000
1.500
2.000
2.500
3.000
0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600
Time, sec.
Y, m
eter
s
0.0000.5001.0001.5002.0002.5003.000
0.000 5.000 10.000 15.000
X position
Y po
sitio
n
X Position vs. Time
0.000
2.000
4.000
6.000
8.000
10.000
12.000
0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600
Time, sec.X,
met
ers
Physlets
• Exploration 3.5, illustrating projectile motion
Conceptual Quick QuizHow do the landing speeds compare?
Ball 1 thrown upwards.Ball 2 thrown downwards.Magnitude of angle is the same.