# PROJECTILE MOTION September 2425, 2015 So far, we

PROJECTILE MOTION September 2425, 2015 So far, we have studied free fall the vertical (up/down) motion of an object that only experiences force due to gravity. What if I gave a freely falling object an initial horizontal velocity? Would the horizontal velocity affect the up / down motion of the object? Watch the Myth Busters compare the rate of falling of a dropped bullet versus a bullet fired from a gun Watch this And this Conclusions Horizontal motion does? NOT affect vertical motion. We will also see that vertical motion does NOT affect horizontal motion. This means we can solve projectile motion problems by dealing with horizontal and vertical motion separately.

Horizontally Launched Projectiles If a ball rolls along the table with constant horizontal velocity, then the moment it leaves the table, it has the same horizontal velocity with which it rolled along the table and zero vertical velocity. In the horizontal direction, there are no forces on the motion which means no acceleration. Horizontal velocity remains CONSTANT. The ball continues to travel horizontally through the air at exactly the same speed which it was rolling on the table. Horizontally Launched Projectiles If a ball rolls along the table with constant horizontal velocity, then the moment it leaves the table, it has the same

horizontal velocity with which it rolled along the table and zero vertical velocity. In vertical direction there is gravitational acceleration. The projectile accelerates downward at exactly the same rate as it would if it were just dropped. When these two motions are combined - vertical free fall motion and uniform horizontal motion - the trajectory will be a parabola. click me Projectiles Launched at an Angle Often, the projectiles are launched at an angle. To solve the problem, we resolve this initial velocity into its vy horizontal and vertical components. Horizontal component vx is constant throughout the motion. v

q vx Vertical component vy is decreasing on the way up, becoming zero at the top, and increasing on the way down. click me Horizontal component of motion for a projectile is completely independent of the vertical component of the motion. Their combined effects produce the variety of curved paths - parabolas that projectile follow. Zookeeper who found the special way to feed monkey banana. The zookeeper aims atacting the monkey If there was no gravity on

and shoots the banana fast . either the banana or thevery monkey, The The zookeeper banana reaches aims above the monkey the banana moves in a straight line and monkeys before

thehead.The monkey has banana misses very the monkey does not fallfallen once he the monkey, far. over head. lets go ofmoving the tree. As his such, a banana passes far above theatmonkey's

head bananaas aimed directly the monkey as was willit hit theoriginally monkey.aimed. The zookeeper aims at the monkey and shoots the banana with a slow speed . Banana hits 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. 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. Check Your Understanding -- The Truck and The Ball Imagine a pickup truck moving with a constant speed along a city street. In the course of its motion, a ball is projected straight upwards by a launcher located in the bed of the truck. Imagine as well that the ball does not encounter a significant amount of air resistance. Where will the ball land? 1) In front of the truck, 2) In the truck, 3) Behind the truck, 4) We need to know the velocity of th e truck and ball to answer How do you know? Range of Projectile Motion (when starting and ending height are equal) 0 75 600

450 300 R = 2 vi2 sin cos the same range is obtained for two projection angles that add up to 900 Projectile thrown with the same speed at 300 and 600 will have the same range. The one at 300 remains in the air for a shorter time. This is our only new equation! 150 What if we have air resistance? IDEAL PATH ACTUAL

PATH Air resistance shortens the range of the object, and the path is no longer a parabola. You wont need to mathematically solve this, but you DO need to be able to describe how air resistance affects the motion. Check your understanding If a projectile launches and lands at the same height, what affects how far it travels? Initial speed and angle What affects how long a projectile stays in the air? Height of launch relative to landing, and

the vertical component of initial velocity. Check your understanding How does a projectiles vertical velocity change over time? It becomes more negative. How does a projectiles horizontal velocity change over time? It doesnt change (if air resistance is ignored) How does a projectiles acceleration change over time? It doesnt change (always 9.81 m/s2 down)

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