7 What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory- does not have any propulsion when in flightExamples:Football, baseball, tennis ball, etcBulletsSnow boarders in a half pipeCliff divers
10 Did you notice?The projectiles hit the ground at the same time regardless of horizontal velocityObject accelerates downwards (at 9.81 m/s2 – acceleration due to gravity)Horizontal displacement stays constant throughout motion
11 Conclusions about Projectile motion The horizontal component of a projectile’s velocity is constant (no acceleration)Projectile experiences constant downwards acceleration (gravity)Horizontal and vertical motion of a projectile are independent of each other (except they have a common time)
14 Important Variables Time – Δt Velocity – v Height – Δdy Distance – ΔdX Acceleration – aLaunch Angle - θ
15 Strategy to Solving Projectile Motion Problems Analyze horizontal motion and vertical motion independentlySeparate the velocity vector into x- and y- componentsRemember: Time is common between them
16 Horizontal motion:- Constant velocity (0 accel.) in the x direction- Equation : v = d/tVertical motion:- Constant acceleration m/s2 [down]- Use the accel. equations we used previously
17 Two Types of Problems: One Dimensional Problems (no horiz Two Types of Problems: One Dimensional Problems (no horiz. Velocity) Case 1: Object dropped from rest Case 2: Object thrown directly upwards Two Dimensional Problems: Case 3: Rolled over an edge Case 4: Shot at an angle Let’s analyze the four cases!
18 For Two Dimensional Problems: Break the initial velocity into horizontal and vertical components (using the given angle and trigonometry) vy θ vx
21 Example Question (Case 3) A tennis ball is rolled off a counter at 8 m/s, what will it’s position be after 3s? Example Question (Case 4) A golfer strikes a golf ball on level ground. The ball leaves the ground with an initial velocity of 42 m/s [32o above the horizontal]. a) What will the ball’s position be after 4 s? b) What will be the maximum height attained?