PROJECTILE MOTION PROJECTILES n Objects that are thrown

PROJECTILE MOTION

PROJECTILES n Objects that are thrown or launched into the air and are subject to gravity are called projectiles. n Projectile motion is the curved path that an object follows when thrown, launched, or otherwise projected near the surface of Earth.

n Two-dimensional motion includes objects which are moving in two directions at the same time, such as a projectile, which has both horizontal and vertical motion.

n These two motions of a projectile are completely independent of one another, and can be described by q q constant velocity in the horizontal direction free fall in the vertical direction.

n We subscript any quantity which is horizontal with an x (such as vx), and we subscript any quantity which is vertical with a y (such as vy. )

Projectile Motion n The motion of a projectile can be broken down into: q q constant velocity and zero acceleration in the horizontal direction changing vertical velocity due to the acceleration of gravity.

n Projectile motion is free fall with an initial horizontal velocity. n The yellow ball is given an initial horizontal velocity and the red ball is dropped. Both balls fall at the same rate. q An object dropped an object fired horizontally will reach the ground at the same time.

n Bullet Dropped vs. Bullet Fired

Kinematic Equations for a Projectile Horizontal motion ax = 0 Vertical motion ay = g = - 10 m/s 2 vyf = vyi + a t x = vxt

A ball is thrown horizontally from the roof of a building 75 m tall with a speed of 4. 6 m/s. a. b. How much later does the ball hit the ground? How far from the building will it land? Answers: a. 3. 9 s b. 18 m

Kinematic Equations for Projectiles n Projectiles Launched Horizontally q The initial vertical velocity is 0. q The initial horizontal velocity is the initial velocity. n Projectiles Launched At An Angle q Resolve the initial velocity into x and y components. q The initial vertical velocity is the y component. q The initial horizontal velocity is the x component.

v vy vy v v vx vx vy v n Notice that the length of the horizontal velocity, since they are constant. n The vertical velocity decreases as the ball rises and increases as the ball falls

Pre-Lecture Quiz 03 -11 From the same height (and at the same time), one ball is dropped another ball is fired horizontally. Which one will hit the flat ground first? (A) the “dropped” ball (B) the “fired” ball (C) they both hit at the same time (D) it depends on how hard the ball was fired (E) it depends on the initial height Pre-Lecture Quiz 03

11 Kinematics in Two Dimensions: Vectors 03 At what angle should a water-gun be aimed in order for the water to land with the greatest horizontal range? (A) 0° (B) 30° (C) 45° (D) 60° Kinematics in Two Dimensions:

16 Kinematics in Two Dimensions: Vectors 03 A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff. A stop watch measures the stone's trajectory time from the top of the cliff to the bottom to be 4. 3 s. What is the height of the cliff? (A) 22 m (B) 43 m (C) 77 m (D) 91 m Kinematics in Two Dimensions:

Pre-Lecture Quiz 03 -13 A projectile is launched from the ground at an angle of 30 o. At what point in its trajectory does this projectile have the least speed? A) just after it is launched B) at the highest point in its flight C) just before it hits the ground D) halfway between the ground and the highest point E) speed is always constant Pre-Lecture Quiz 03

14 Kinematics in Two Dimensions: Vectors 03 If a ball is thrown with a velocity of 25 m/s at an angle of 37° above the horizontal, what is the vertical component of the velocity? (A) 12 m/s (B) 15 m/s (C) 19 m/s (D) 25 m/s Kinematics in Two Dimensions:

06 Kinematics in Two Dimensions: Vectors 03 A projectile is launched with an initial velocity of 60. 0 m/s at an angle of 30. 0° above the horizontal. What is the maximum height reached by the projectile? (A) 23 m (B) 46 m (C) 69 m (D) 92 m Kinematics in Two Dimensions: