1. PDT 180 ENGINEERING SCIENCE Vectors And Scalars (Continue)

2. P ROJECTILE M OTION A projectile is an object moving in two dimensions under the influence of Earth's gravity. Its path is a parabola.

3. Neglect air resistance. Consider motion only after release and before it hits. Analyze the vertical and horizontal components separately (Galileo). No acceleration in the horizontal, so velocity is constant. Acceleration in the vertical is – 9.8 m/s 2 due to gravity and thus velocity is not constant. Object projected horizontally will reach the ground at the same time as one dropped vertically.

4. E QUATIONS FOR P ROJECTILE M OTION Horizontal Vertical a x = 0 a y = - g v x = constant

5. I NITIAL V ELOCITY If the ball returns to the y = 0 point, then the velocity at that point will equal the initial velocity. At the highest point, v 0 y = 0 and v = v x0

6. Module 7 - 5 E XAMPLE 3A A football is kicked at an angle of 50.0 0 above the horizontal with a velocity of 18.0 m / s. Calculate the maximum height. Assume that the ball was kicked at ground level and lands at ground level. at top:

7. Module 7 - 9 E XAMPLE 4A A football is kicked at an angle of 50.0 0 above the horizontal with a velocity of 18.0 m / s. The football hits a window in a house that is 25.0 m from where it was kicked. How high was the window above the ground. Time to hit the window:

8. Module 7 - 10 E XAMPLE 4 B What is the final velocity and angle of the football that hit the window in Example 4 A. below x axis

9. Module 7 - 12 Example 5. (35) A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge 235 m below. If the plane is traveling horizontally with a speed of 250 km /h (69.4 m / s) how far in advance of the recipients (horizontal distance) must the goods be dropped (Fig. 3–37a)?. Coordinate system is 235 m below plane

10. Module 7 - 13 Projectile Motion Is Parabolic In order to demonstrate that projectile motion is parabolic, the book derives y as a function of x. When we do, we find that it has the form: This is the equation for a parabola.