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Ch 3 part 2: Projectile Motion and Vectors in 2 dimensions Projectile Motion In studying more general motion of objects moving through the air, we consider 2 dimensions (horizontal and vertical) together, yet independent, to create curved paths. Although air resistance is important, it will be most often ignored. Projectiles will be studied as they move freely in the air under the influence of gravity alone. (at g=9.80m/s2 downward) Horizontal vs Vertical motion Galileo first showed that horizontal and vertical components of motion can be studied separately. Notice the vertical positions of each ball in the picture. Horizontal direction of motion In the horizontal direction there is no acceleration (ignoring air resistance) so the horizontal component of velocity, vx remains constant and equal to its initial value, vx0 Horizontal displacement is given by x = vx0 t An object projected horizontally will reach the ground in the same time as an object dropped vertically from same h. http://www.youtube.com/watch?v=D9wQVIEdKh 8 Vertical direction of motion Objects leaving their support and falling, experience acceleration downward instantly due to earth’s gravity, a=g=9.80m/s2 near earth’s surface. Vy is initially zero, but experiences continual increase until it hits the ground. If we consider y positive upward, then ay = -g and from v=v0 +at, we get vy = -gt since vy0 = 0. Vertical displacement is given as y = -½ gt2 . Illustrations of Projectiles Notice horizontal and vertical displacements here. What happens to each component over time? What would you get if you combined Horizontal and vertical displacement or Velocity components with Pythagorean Theorem? Instantaneous velocity! Projectiles launched at angles For projectiles launched at some angle into the air above the horizontal, only the y component of velocity experiences acceleration. Therefore it will decrease on the way up, come to zero at the top, and increase on the way down. The horizontal component of the initial velocity remains constant throughout the trip. Can a projectile like this ever land “straight down”?