Agenda Warm-Up More about Science Fair Topics Intro to Projectile Motion Notes: Projectile Motion Components of Projectile Motion Horizontal Initial Velocity Angled Initial Velocity Quizzes Returned
Objectives: We Will Be Able To… Recognize examples of projectile motion. Describe the path of a projectile as a parabola. Resolve vectors into their components and apply the kinematic equations to solve problems involving projectile motion.
Warm-Up: Two lemmings stand on a cliff. Lemming A steps of the edge at the exact same time that Lemming B runs and leaps straight out (horizontally). Which lemming, if either, hits the ground first? Write 1-2 sentences explaining your thoughts, then discuss at your table.
Objects that are thrown or launched into the air and are subject to gravity are called projectiles. Projectile motion is free fall with an initial horizontal velocity. The path of a projectile is a curve called a parabola (the path shown below).
Projectile Motion Because projectile motion is free fall with initial velocity, we can analyze the horizontal and vertical components separately. Vertically: the object has some initial velocity, which changes with the acceleration due to gravity. Horizontally: the object has some initial velocity, which does not change (assuming no air resistance).
Projectile Motion Note: v x =constant v y changes with gravity
Problem Solving Projectile Motion can be broken up into two categories. Either: The initial velocity is perfectly horizontal (today) The initial velocity is at an angle
Problem Solving with Horizontal Initial Velocity All of the one-dimensional motion equations from Chapter 2 still apply. In the y-direction, the object has no initial velocity (v y,i =0). Essentially the object is falling from rest. In the x-direction, the object has an initial velocity that remains constant.
Problem Solving with Horizontal Initial Velocity (p. 100) Note the new subscripts. Time is the only variable in both the x- and y- directions, so you will often need to find time in one dimension, and use it to solve for the missing variable in the other dimension.
Practice Problem The Royal Gorge Bridge in Colorado rises 321 m above the Arkansas River. Suppose you kick a little rock horizontally off the bridge. The rock hits the water such that the magnitude of the horizontal displacement is 45.0 m. Find the speed at which the rock was kicked.
Warm Up: Components A soccer ball is kicked with an initial velocity of 5.00 m/s at an angle of 33.0 degrees above the horizontal. What are the horizontal and vertical components of this velocity? (v x and v y )
Schedule of the Next Week Tomorrow: Problem Solving Practice Friday: Lab/ Chapter 3 Review Monday-Tuesday: Library Research Wednesday: Ch. 3 Test
A note about g g is the acceleration due to gravity: 9.81 m/s 2 In previous formulas, where the acceleration was the acceleration due to gravity, we needed to indicate that gravity accelerated in the negative direction a = -9.81 m/s 2 In these formulas, g is given the formula, so there is no need to add a negative sign. These formulas take into account that gravity is in the negative direction. g = 9.81 m/s 2
The differences between launching at an angle as opposed to launching horizontally: Velocity in the x-direction is a component of the initial velocity. There is now initial velocity in the y-direction.
Practice Problem In a scene in an action movie, a stuntman jumps from the top of one building to the top of another building 4.0 m away. After a running start, he leaps at an angle of 15 degrees with respect to the flat roof while traveling at 5.0 m/s. Will he make it to the other roof, which is 2.5 m shorter than the building he jumps from?
Wrap-Up: Did we meet our objectives? Recognize examples of projectile motion. Describe the path of a projectile as a parabola. Resolve vectors into their components and apply the kinematic equations to solve problems involving projectile motion.