1. Two Dimensional Dynamics

2. Break 2-D problem into two 1-D problemsy x
2-Dimensions
X and Y are INDEPENDENT!
Break 2-D problem into two D problems 7

3. Kinematics in Two Dimensions
x = x0 + v0xt + 1/2 axt2
vx = v0x + axt
vx2 = v0x2 + 2ax x
y = y0 + v0yt + 1/2 ayt2
vy = v0y + ayt
vy2 = v0y2 + 2ay y
x and y motions are independent!
They share a common time t 21

4. Projectile Motion Demo
One marble is given an initial horizontal velocity, the other simply dropped. Which marble hits the ground first?
A) dropped
B) pushed
C) They both hit the ground at the same time
Could add y(t) equation here change to marble equation
When ball hits depends on y only!
y(t) = y0 + vyo + ½ ay t
Same for both balls! 35

5. Example: ball thrown from cliff
Use y components to find time
vo= 20 m/s
Use x velocity and time to find horizontal distance
60m

6. Example: projectile Break Vo into x & y components Vo=30m/s Vo=30m/s
200 Δx
Break Vo into x & y components
Vo=30m/s
200

7. Example: projectile
Vo=30m/s Δy
200 Δx

8. Will the ball get over the tree?
Example: golf shot
Will the ball get over the tree?
Vo=50m/s
400
20m
Vo=50m/s
400
30m

9. Will the ball get over the tree?
Example: golf shot
Will the ball get over the tree?
20m
Vo=50m/s
400
30m

10. Summary of Concepts X and Y directions are Independent!
Position, velocity and acceleration are vectors
“Share” t
F = m a applies in both x and y direction
Projective Motion
ax = 0 in horizontal direction
ay = g in vertical direction 50