Projectile & Uniform Circular Motion Guided NotesName:______
Myth Busters fired bullet vs. dropped bullet
Conclusions: Horizontal motion ______vertical motion. We will also see that vertical motion ______horizontal motion. This means we can solve projectile motion problems by dealing with horizontal and vertical motion ______.
Horizontally Launched Projectiles
A ball rolling off the table is an excellent example of an object thrown into the air with horizontal initial velocity (velocity at the time when the object is launched). The ball becomes airborne when leaving the table.
If the 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 ______.
Horizontal velocity remains ______. The ball continues to travel horizontally through the air at exactly the same speed which it was rolling on the table.
In vertical direction there is ______. The projectile accelerates downward at ______ 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 ______.
Helicopter example
How does the horizontal motion of a person dropped from a helicopter moving at constant speed compare to the motion of the helicopter?
How does the vertical component of a person dropped from a helicopter moving at constant speed compare to the motion of a person that falls from a stationary helicopter?
What does the overall motion look like?
Draw the motion.
What happens to the motion of the falling person if the helicopter changes speed?
Does the time in the air change?
Does the horizontal range of motion change?
Does the vertical velocity change?
Projectiles Launched at an Angle
Often, the projectiles are launched at an angle. To solve the problem, we resolve this initial velocity into its ______.
Horizontal component ______x is ______throughout the motion.
Vertical component ______is decreasing on the way up, becoming zero at the top, and increasing on the way down.
Horizontal component of motion for a projectile is ______of the vertical component of the motion. Their combined effects produce the variety of curved paths - parabolas that projectile follow.
Monkey and Banana example
Where do you aim if you are shooting a banana to a monkey that drops from the tree the same moment you shoot the banana? Why?
Does it matter how fast the banana goes?
Check your understanding – the ball and the truck
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 the truck and ball to answer
How do you know?
Range of Motion
______
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.
Range of motion with air resistance
What if we have air resistance?
Air resistance ______, and the path is no longer a parabola. You won’t 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?
What affects how long a projectile stays in the air?
How does a projectile’s vertical velocity change over time?
How does a projectile’s horizontal velocity change over time?
How does a projectile’s acceleration change over time?
Projectile Motion Problem Solving
To solve projectile motion problems, you must separate the horizontal and vertical components of motion.
1)Resolve the launch velocity to find the vix and viy. (Use SOH CAH TOA)
2)Divide your paper into two sections – one for horizontal and one for vertical
3)Write the relevant equations and known variables in the appropriate sections
4)Recognize that horizontal and vertical sides are linked by time in the air. You may use time to find other variables on either section.
Problem 1: Soccer Ball kick
A player kicks a soccer ball from ground level with an initial velocity of 27.0 m/s, 30o above the horizontal. Find each of the following. Assume that air resistance is negligible.
a)The ball’s hang time
b)The ball’s maximum height
c)The horizontal distance the ball travels before hitting the ground.
Problem 2: Giraffe assembly line
Lucy and her friend are working at an assembly plant making wooden toy giraffes. At the end of the line, the giraffes go horizontally off the edge of a conveyor belt and fall into a box below. If the box is 0.60 m below the level of the conveyor belt and 0.40 m away from it, what must be the horizontal velocity of giraffes as they leave the conveyor belt?
Problem 3: Rock thrown from a cliff 1
A rock is thrown from a 50.0 m high cliff with an initial velocity of 7.0 m/s at an angle of 53o above the horizontal. Finds its velocity when it hits the ground.
Problem 4: Rock thrown from a cliff 2
You throw a stone horizontally at a speed of 5.0 m/s from the top of a cliff that is 78.4 m high.
a)How long does it take the stone to reach the bottom of the cliff?
b)How far from the base of the cliff does the stone hit the ground?
c)What are the horizontal and vertical components of the stone’s velocity as it hits the ground?
Problem 5: Darts
A dart player throws a dart horizontally at 12.4 m/s. The dart hits the board 0.32 m below the height from which it was thrown. How far away is the player from the board?
Uniform Circular Motion Guided Notes
Check your understanding
When a wheel rotates about a fixed axis, do all the points on the wheel have the same tangential speed?
Do they all have the same velocity?
Circular Motion Equations
Where
Vt = tangental velocity
R = radius
T = period (time required to make one complete circle)
Ac = centripetal acceleration
We Do
•The radius of a spacecraft orbiting earth is 6.67 x 106 m. If it orbits earth in 5292 seconds, what is the velocity of the spacecraft?
- Jimmie Johnson is driving his #48 Lowe’s NASCAR around a bend that has a radius of 70 meters. It takes him 30 seconds to travel the track. What was the centripetal acceleration of Jimmie John’s #48 Lowe’s NASCAR?
You Do
a. A girl sits on a tire that is attached to an overhanging tree limb by a rope. The girl’s father pushes her so that her centripetal acceleration is 3.0 m/s2. If the length of the rope is 2.1 m, what is the girl’s tangential speed?
b. A boy swings a yo-yo horizontally above his head so that the yo-yo has a centripetal acceleration of 1.5m/s2. If the yo-yo’s tangential speed is 1.1m/s, what is the length of the yo-yo?
c. Correct the following statement: The racing car rounds the turn at a constant velocity of 145 km/h.