1. PHYS 1443 – Section 501 Lecture #5
Wednesday, February 4, 2004
Dr. Andrew Brandt
Motion in Two Dimensions
Vector Components
2D Motion under constant acceleration
Projectile Motion
Wednesday, Feb. 4, 2004
PHYS , Spring 2004
Dr. Andrew Brandt

2. Announcements
Your lab-sessions began Monday, Feb. 2. Be sure to attend the lab classes (20% of your grade)
Homework: 21/40 (out of 44) have submitted some answers
HW1 due midnight tonight
HW2 (Ch 3) due 2/11
Read the text book!
Wednesday, Feb. 4, 2004
PHYS , Spring 2004
Dr. Andrew Brandt

3. Vector Addition
Find the resultant vector which is the sum of A=(2.0i+2.0j) and B =(2.0i-4.0j) OR
Magnitude
Direction
Find the resultant displacement of three consecutive displacements: d1=(15i+30j +12k)cm, d2=(23i+14j -5.0k)cm, and d1=(-13i+15j)cm
Magnitude
Wednesday, Feb. 4, 2004
PHYS , Spring 2004
Dr. Andrew Brandt

4. Kinetic Quantities in 1d and 2d
1 Dimension
2 Dimension
Displacement
Average Velocity
Inst. Velocity
Average Acc.
Inst. Acc.
Wednesday, Feb. 4, 2004
PHYS , Spring 2004
Dr. Andrew Brandt

5. 2-dim Motion Under Constant Acceleration
Position vectors in x-y plane:
Velocity vectors in x-y plane:
Velocity vectors in terms of acceleration vector
Velocity vector components
Putting them together in a vector form
Wednesday, Feb. 4, 2004
PHYS , Spring 2004
Dr. Andrew Brandt

6. 2-dim Motion Under Constant Acceleration
How are the position vectors written in terms of velocity and acceleration vectors?
Position vector components
Putting them together in vector form
Regrouping above results
Wednesday, Feb. 4, 2004
PHYS , Spring 2004
Dr. Andrew Brandt

7. Example: 2-D Kinetic Eq.of Motion
A particle starts at origin when t=0 with an initial velocity v=(20i-15j)m/s. The particle moves in the xy plane with ax=4.0m/s2. Determine the components of velocity vector at any time, t.
Compute the velocity and speed of the particle at t=5.0 s.
Magnitude
Wednesday, Feb. 4, 2004
PHYS , Spring 2004
Dr. Andrew Brandt

8. Example in 2-D Kinetic EoM cont’d
Direction
Determine the x and y components of the particle at t=5.0 s.
Can you write down the position vector at t=5.0s?
Wednesday, Feb. 4, 2004
PHYS , Spring 2004
Dr. Andrew Brandt

9. Projectile Motion
2-dim motion of an object under gravitational acceleration with the assumptions
Free fall acceleration, -g, is constant over the range of the motion
Air resistance and other effects are negligible
Superposition of two motions
Horizontal motion with constant velocity ( no acceleration )
Vertical motion under constant acceleration ( g )
monkey in tree
Wednesday, Feb. 4, 2004
PHYS , Spring 2004
Dr. Andrew Brandt

10. Projectile Motion
The only acceleration in this motion. It is a constant!!
Wednesday, Feb. 4, 2004
PHYS , Spring 2004
Dr. Andrew Brandt

11. Show that projectile motion is a parabola
x-component
y-component
In projectile motion, the only acceleration is a gravitational one whose direction is always toward the center of the earth (downward).
ax=0
Plug t into
the above
Wednesday, Feb. 4, 2004
PHYS , Spring 2004
Dr. Andrew Brandt