In this section you will: Recognize that the vertical and horizontal motions of a projectile are independent. Draw a free body diagram for an object in projectile motion Recognize the forces are acting on an object in projectile motion. Explain how the trajectory of a projectile depends upon the frame of reference from which it is observed. Section 6.1-1

Projectile Motion If you observed the movement of a golf ball being hit from a tee, a frog hopping, or a free throw being shot with a basketball, you would notice that all of these objects move through the air along similar paths, as do baseballs, and arrows. Each path is a curve that moves upward for a distance, and then, after a time, turns and moves downward for some distance. You may be familiar with this curve, called a parabola, from math class. Section 6.1-2

Projectile Motion An object shot through the air is called a projectile. A projectile can be a football or a drop of water. You can draw a free-body diagram of a launched projectile and identify all the forces that are acting on it. Section 6.1-3

Projectile Motion Projectile Motion Free Diagram Fg= mg If air resistance is negated, the only force acting on object undergoing projectile motion is the force of gravity. Section 6.1-3

Projectile Motion The force of gravity is what causes the object to curve downward in a parabolic flight path. Its path through space is called its trajectory. Section 6.1-4

Click image to view movie. Independence of Motion in Two Dimensions Click image to view movie. Section 6.1-5

Projectiles Launched at an Angle The adjoining figure shows the separate vertical- and horizontal- motion diagrams for the trajectory of the ball. Section 6.1-7

The Flight of a Ball If a ball is launched horizontally from the counter top, how does the time it takes to hit the ground compare to the time a ball will take to fall straight down from the same height? Test To Find Out Section 6.1-13

Launched Ball The motion horizontally is separate from the motion vertically. The time to fall is based on df=di+vit+1/2at2 Dropped ball The motion is based on df=di+vit+1/2at2

Launched Ball di= height of counter= 1m df=0 Vi (applies to the y direction=0) a=-9.8m/s2 Dropped Ball di= height of counter= 1m df=0 Vi (applies to the y direction=0) a=-9.8m/s2

Notice both equations and variables are the same!!! They should hit the ground at the same time which can be found by using the following. 0= 1m + 0t +1/2(-9.8m/s2)t2 0= 1m + (-4.9m/s2)t2 -1m/-4.9m/s2= t2 t= (0.2s2)^1/2 t=0.45s

The launched balls velocity can also be found by measuring its horizontal displacement over the time it falls. Because it is not accelerating in the horixontal diretion the basic displacement eauation can be used. df=di + vit, df= 0, where di=0

Trajectories Depend upon the Viewer The path of the projectile, or its trajectory, depends upon who is viewing it. Suppose you toss a ball up and catch it while riding in a bus. To you, the ball would seem to go straight up and straight down. But an observer on the sidewalk would see the ball leave your hand, rise up, and return to your hand, but because the bus would be moving, your hand also would be moving. The bus, your hand, and the ball would all have the same horizontal velocity. Section 6.1-36

Question 1 A boy standing on a balcony drops one ball and throws another with an initial horizontal velocity of 3 m/s. Which of the following statements about the horizontal and vertical motions of the balls is correct? (Neglect air resistance.) Section 6.1-38

Question 1 A. The balls fall with a constant vertical velocity and a constant horizontal acceleration. B. The balls fall with a constant vertical velocity as well as a constant horizontal velocity. C. The balls fall with a constant vertical acceleration and a constant horizontal velocity. D. The balls fall with a constant vertical acceleration and an increasing horizontal velocity. Section 6.1-38

Answer 1 Reason: The vertical and horizontal motions of a projectile are independent. The only force acting on the two balls is the force of gravity. Because it acts in the vertical direction, the balls accelerate in the vertical direction. The horizontal velocity remains constant throughout the flight of the balls. Section 6.1-39

Question 2 Which of the following conditions is met when a projectile reaches its maximum height? A. The vertical component of the velocity is zero. B. The vertical component of the velocity is maximum. C. The horizontal component of the velocity is maximum. D. The acceleration in the vertical direction is zero. Section 6.1-40

Answer 2 Reason: The maximum height is the height at which the object stops its upward motion and starts falling down, i.e. when the vertical component of the velocity becomes zero. Section 6.1-41

Question 3 Suppose you toss a ball up and catch it while riding in a bus. Why does the ball fall in your hands rather than falling at the place where you tossed it? Section 6.1-42

Answer 3 Trajectory depends on the frame of reference. For an observer on the ground, when the bus is moving, your hand is also moving with the same velocity as the bus, i.e. the bus, your hand, and the ball will have the same horizontal velocity. Therefore, the ball will follow a trajectory and fall back into your hands. Section 6.1-43