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PHYS 1443 – Section 501 Lecture #5

Learn about motion in two dimensions, vector addition, kinetic quantities in 1D and 2D, and projectile motion examples in this PHYS 1443 lecture. Understand how to find resultant vectors and displacement magnitudes, position and velocity vectors, and more!

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PHYS 1443 – Section 501 Lecture #5

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

  4. Kinetic Quantities in 1d and 2d PHYS 1443-501, 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 PHYS 1443-501, 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 PHYS 1443-501, 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 PHYS 1443-501, 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? PHYS 1443-501, 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 PHYS 1443-501, Spring 2004 Dr. Andrew Brandt

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

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