BELLWORK 1/04/17 What is a projectile?

ANSWER Any moving object upon which the only force acting on it is gravity.

Motion In Two Dimensions can be considered constant. Projectile Motion Motion In Two Dimensions We restrict ourselves to objects thrown near the Earth’s surface so that gravity can be considered constant.

A projectile is defined as any moving object upon which the only force acting on it is gravity. A projectile is any object that once projected or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity.

Projectile Motion and Inertia "How in the world can an object be moving upward if the only force acting upon it is gravity?” Newton's laws suggest that forces are only required to cause an acceleration (not a motion). A force is not required to keep an object in motion. (Newton’s 1st Law) In the case of a projectile that is moving upward, there is a downward force and a downward acceleration.

To further investigate a downward force and a downward acceleration of a projectile, consider a cannonball shot horizontally from a very high cliff at a high speed. And suppose for a moment that the gravity switch could be turned off such that the cannonball would travel in the absence of gravity? What would the motion of such a cannonball be like? How could its motion be described?

Now suppose that the gravity switch is turned on and that the cannonball is projected horizontally from the top of the same cliff. Will gravity affect the cannonball's horizontal motion? Will the cannonball travel further, closer, or the same horizontal distance due to the influence of gravity? No, and the same horizontal distance, gravity only effects its vertical motion.

Projectile Problem There is an interesting monkey down at the zoo. The monkey spends most of its day hanging from a limb of a tree. The zookeeper feeds the monkey by shooting bananas from a banana cannon to the monkey in the tree. This particular monkey has a habit of dropping from the tree the moment that the banana leaves the muzzle of the cannon. The zookeeper is faced with the dilemma of where to aim the banana cannon in order to hit the monkey. If the monkey lets go of the tree the moment that the banana is fired, then where should she aim the banana cannon? Should the zookeeper aim the banana above the monkey, at the monkey, or below the monkey.

To ponder this dilemma consider the following: Shoot at the monkey in a gravity free environment. In the absence of gravity, the banana moves in a straight line path (and does not experience any downward acceleration) and the monkey does not fall once he lets go of the tree.

Shoot the banana above the monkey in the presence of gravity. The banana moves in a parabolic path in the presence of gravity. In the presence of gravity, the monkey also accelerates downward once he lets go of the limb. Both banana and monkey experience the same acceleration since gravity causes all objects to accelerate at the same rate regardless of their mass. Since both banana and monkey experience the same acceleration each will fall equal amounts. The banana misses the monkey, moving over his head as it was originally aimed.

Shoot at the Monkey at a Fast Speed with Gravity On Since the banana left the muzzle moving very fast, the banana reaches the monkey before the monkey has fallen very far.

Shoot at the Monkey at a Slow Speed with Gravity On Since the banana left the muzzle moving very slow, the banana reaches the monkey after the monkey has fallen considerably far. In conclusion, the key to the zookeeper's dilemma is to aim directly at the monkey.

Characteristics of Projectiles Projectile motion is a combination of horizontal motion and vertical motion. (Two- dimensional motion) The horizontal motion of a projectile is constant because there are no horizontal forces acting on it other than its initial velocity.

The vertical motion of a projectile is nothing more than free fall with a constant downward acceleration due to gravity. (We are neglecting air resistance)

The path of a projectile is called its trajectory.   The trajectory of a projectile in free fall is a parabola.

A projectile, once projected, continues in motion by its own inertia and is influenced only by the downward force of gravity.

An object projected horizontally will reach the ground in the same time as an object dropped vertically. No matter how large the horizontal velocity is, the downward pull of gravity is always the same.

Projectile Equations – We can use our Kinematic Equations from Ch.2 Horizontal Motion Vertical Motion Vf = aΔt Vf2 = 2aΔy Δy = 1/2a(Δt)2 Δx = ViΔt Vi = Vf = Constant .

Why does the horizontal component of a projectile’s motion remain constant? Because no force acts on it horizontally.

Why does the vertical component of a projectile’s motion undergo change? Because gravity is pulling it downward.

Classwork – Horizontally Launched Projectiles Complete #’s 1-4 on Page 99 Add Chapter 3 Formulas to index card. Use Page 854 in book.

Projectiles Launched at an Angle Complete the PHET Lab Simulation

Projectiles Launched at An Angle Maximum range is achieved if the projectile is fired at an angle of_____ degrees with respect to the horizontal.