Presentation on theme: "Projectile Motion Projectile motion: a combination of horizontal motion with constant horizontal velocity and vertical motion with a constant downward."— Presentation transcript:
2 Projectile MotionProjectile motion: a combination of horizontal motion with constant horizontal velocity and vertical motion with a constant downward acceleration due to gravity.Projectile motion refers to the motion of an object that is thrown, or projected, into the air.We restrict ourselves to objects thrown near the Earth’s surface so that gravity can be considered to be constant.
4 Projectile MotionThe motion of a projectile is determined only by the object’s initial velocity and gravity.The vertical motion of a projected object is independent of its horizontal motion.The vertical motion of a projectile is nothing more than free fall.The one common variable between the horizontal and vertical motions is time.
6 Gravity only affects vertical motion. Projectile motion problems are best solved bytreating horizontal and vertical motion separately.*IMPORTANT*Gravity only affects vertical motion.There are two general typesof projectile motion situations.1. object launched horizontally2. object launched at an angle
7 Path of a ProjectileA projectile moves horizontally with constant velocity while being accelerated vertically. A right angle exists between the direction of the horizontal and vertical motion; the resultant motion in these two dimensions is a curved path.The path of a projectile is called its trajectory.The trajectory of a projectile in free fall is a parabola.
8 Rx = vxt h = 0.5gt2 Object Launched Horizontally horizontal vertical vx = initial horizontal velocityh = initial heightabove groundt = total time in the airRx = horizontal rangeIMPORTANT FACTSThere is no horizontal acceleration.There is no initial vertical velocity.The horizontal velocity is constant.Time is the same for both vertical and horizontal.horizontalverticalRx = vxth = 0.5gt2
9 Motion in 2D…Throw a ball on a moving truck demoMonkey shooting
16 When a projectile is launched at an angle the object moves both up and down and side to side at the same time
17 The vertical component (Vy) controls how high the object rises The vertical component (Vy) controls how high the object rises. This is the objects maximum height. It occurs half way through the projectiles path **The path of a projectile is called its trajectory
18 This means, when a projectile is launched at an angle, it’s velocity has a vertical and horizontal component
19 Since the maximum height (dy) occurs half way through the trajectory, vertical equations use time for only half the trip total time=4sty=2s
20 The horizontal component (Vh) controls how far over the object travels The horizontal component (Vh) controls how far over the object travels. This is called the object’s range. It occurs at the end of the entire trajectory.
21 Since the object’s range (dx), occurs over the entire trip, horizontal equations must use the time for the total trip.tx=4s
22 Changing the angle at which the projectile is launched effects the vertical and horizontal distances the object travels
26 Path of a Projectile vo = initial velocity or resultant velocity vx = horizontal velocityvyi = initial vertical velocityvyf = final vertical velocityR= maximum horizontal distance (range)x = horizontal distanceDy = change in vertical positionyi = initial vertical positionyf = final vertical positionq = angle of projection (launch angle)H = maximum heightag = gravity = 9.8 m/s2
27 Path of a ProjectileThe horizontal distance traveled by a projectile is determined by the horizontal velocity and the time the projectile remains in the air. The time the projectile remains in the air is dependent upon gravity.Immediately after release of the projectile, the force of gravity begins to accelerate the projectile vertically towards the Earth’s center of gravity.
28 Path of a ProjectileThe velocity vector vo changes with time in both magnitude and direction. This change is the result of acceleration in the negative y direction (due to gravity). The horizontal component (x component) of the velocity vo remains constant over time because there is no acceleration along the horizontal directionThe vertical component (vy) of the velocity vo is zero at the peak of the trajectory. However, there is a horizontal component of velocity, vx, at the peak of the trajectory.
30 Horizontal velocity component: vx is constant because there is no acceleration in the horizontal direction if air resistance is ignored.
31 Vertical velocity component: At the time of launch:After the launch:If vy positive, direction of vertical motion is up; if vy negative, direction of vertical motion is down; if vy = 0, projectile is at highest point.
32 Horizontal position component: If you launch the projectile horizontally:then vo = vxvyi = 0 m/s = 0o
37 Range and Angle of Projection The range is a maximum at 45 because sin (2·45) = 1.For any angle other than 45, a point having coordinates (x,0) can be reached by using either one of two complimentary angles for , such as 15 and 75 or 30 and 50 .
38 Range and Angle of Projection The maximum height and time of flight differ for the two trajectories having the same coordinates (x, 0).A launch angle of 90° (straight up) will result in the maximum height any projectile can reach.
39 For Situations In Which Dy Positive At any point in the flight: