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 1443-501, Spring 2004 Dr. Andrew Brandt

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 1443-501, Spring 2004 Dr. Andrew Brandt

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 1443-501, Spring 2004 Dr. Andrew Brandt

Kinetic Quantities in 1d and 2d 1 Dimension 2 Dimension Displacement Average Velocity Inst. Velocity Average Acc. Inst. Acc. Wednesday, Feb. 4, 2004 PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

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 1443-501, Spring 2004 Dr. Andrew Brandt

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 1443-501, Spring 2004 Dr. Andrew Brandt

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 1443-501, Spring 2004 Dr. Andrew Brandt

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 1443-501, Spring 2004 Dr. Andrew Brandt

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 1443-501, Spring 2004 Dr. Andrew Brandt

Projectile Motion The only acceleration in this motion. It is a constant!! Wednesday, Feb. 4, 2004 PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

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 1443-501, Spring 2004 Dr. Andrew Brandt