Projectile Motion

Ignoring air resistance, which of the following correctly shows what an object would do if it rolled off a cliff? #1: the object will stop in midair and then fall straight down (like Wile E Coyote) #2: the object will move forward at first, but will eventually fall straight down #3: the object will continue to move forwards the entire time it is falling

The correct answer is….. #3 – the object will continue to move forward the entire time it is falling ▫Why does this happen? ▫Because the object is in projectile motion  When an object is moving in 2 dimensions (vertically and horizontally) but is only affected by gravity  This means that any object in projectile motion is also in free fall ▫The two movements, horizontal and vertical, act independently of each other  One does not effect the other  We will calculate them completely separately

Projectile Motion, an illustration Vertical Motion Horizontal Motion

Horizontal motion (X) As the object leaves the cliff, it does so with an initial horizontal velocity ▫The only way to change this velocity is to put some sort of new force (push or pull) on the object ▫Ignoring air resistance, there is no other force affecting the object so it’s horizontal velocity does not change  So the object continues to move forward at the same speed the entire time it falls

Vertical motion (X) Remember that in projectile motion, the object is in free fall ▫So as soon as it leaves the cliff, gravity is pulling the object down  Acceleration due to gravity affects vertical speed causing it to increase by 10 m/s/s

Horizontal and vertical motion What do you notice about the horizontal velocity vector? What do you notice about the vertical velocity vector? The shape that an object in projectile motion takes is known as a parabola (an arc)

When you are solving projectile motion problems… If you are solving for horizontal motion (x direction), only use: If you are solving for vertical motion (y direction), only use: V = d t V = gt or d = 1/2 gt 2 This is because gravity does not effect horizontal motion This is because gravity is the only thing that affects vertical motion The amount of time that an object falls will be the same for both horizontal and vertical motion - This is because no matter if an object is falling or if it has been thrown, it will fall towards the earth with the same acceleration (10 m/s/s) due to gravity

A projectile Motion problem: A rock is thrown off a cliff with a horizontal speed (V x ) of 20 m/s. It lands 5 seconds later. Determine how high the cliff is and how far the rock fell horizontally Horiz.Vert. V D T Create a chart to help figure out your data

What is the actual speed of the ball before it hits the ground? We found the vertical and horizontal speed of the ball so we can combine the two vectors to find the actual speed 20 m/s 5 m/s

Another problem: A baseball is thrown out of a window with a horizontal speed (V x ) of 45 m/s. It landed 9s later. ▫How high is the window? ▫What was the vertical velocity when it hit the ground? ▫How far away did the ball land? ▫What is the resulting speed of the baseball just before it landed?