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Projectile Motion

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Page 1: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Projectile Motion

Page 2: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

What is a Projectile?• Projectile

– an object that moves along a 2-D curved trajectory

- does not have any propulsion when in flight

Page 3: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight
Page 4: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Yes Examples Non Examples

• Tennis ball• Football• Golf ball• Basketball• Javelin• Jumping out of a car• Cannon ball

• Plane• Rocket• Missile

Page 5: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Projectile Motion Example # 1

Page 6: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

The ball is in free fall vertically and moves at constant speed horizontally!!!

Page 7: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Conclusions about Projectile motion

1) The horizontal component of a projectile’s velocity is constant (no acceleration)

2) Projectile experiences constant downwards acceleration (gravity)

3) Horizontal and vertical motion of a projectile are independent of each other (except they have a common time)

Page 8: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight
Page 9: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Projectile Motion Example # 2

Page 10: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Important Variables

• Time – Δt• Velocity – vi, vf

• Height – Δdy

• Distance – ΔdX

• Acceleration – a• Launch Angle - θ

Page 11: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Strategy to Solving Projectile Motion Problems

• Analyze horizontal motion and vertical motion independently–Separate the velocity vector into x-

and y- components• Remember: Time is common

between them• Use an x/y chart to list givens

Page 12: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Horizontal motion:- Constant velocity (0

accel.) in the x direction- Equation : v = d/t

Page 13: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Vertical motion:- Constant acceleration - 9.81

m/s2 [down]- Use the accel. equations we

derived

Page 14: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Two Types of Problems: One Dimensional Problems (no horiz. Velocity)

Case 1: Object dropped from restCase 2: Object thrown directly upwards

Two Dimensional Problems:Case 3: Rolled over an edgeCase 4: Shot at an angle

Page 15: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

For Two Dimensional Problems:

Break the initial velocity into horizontal and vertical components (using the given angle and trigonometry)

vy

θ

vx

Page 16: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Projectile Motion Example # 3

Page 17: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Example Question 1A tennis ball is rolled off a counter at 8 m/s,

what will it’s position be after 3s?

Example Question 2A golfer strikes a golf ball on level ground. The

ball leaves the ground with an initial velocity of 42 m/s [32o above the horizontal].

a) What will the ball’s position be after 4 s?b) What will be the maximum height attained?

Page 18: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

• Example # 3: A cannonball is fired with velocity of 50.0 m/s [30º above the horizontal]. It is shot at the level battle field which is located 20.0 m below.• a) Calculate the horizontal

displacement of the cannonball.• b) Calculate the impact velocity of the

cannonball

Page 19: Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved trajectory - does not have any propulsion when in flight

Hard Projectile Penetration and Trajectory Stability

Chapter 2: Types of Evidence - Useful Advice · Chapter 2: Types of Evidence ... Blood spatter Glass fracture Fire burn pattern Furniture position Projectile trajectory ... Miscellaneous—laundry

PROJECTILE MOTION A.P..pdf · • The path or trajectory projectiles make is parabolic (neglecting air resistance). • Two independent motions- horizontal and vertical. • Use kinematics

Tennis- Maths Exploration (Final) - IB Revision · First Model Assumptions of the first model The trajectory of the tennis ball is taken to be the ballistic trajectory of a projectile

Physics of ball sports - · PDF filebeach volley, football/soccer, golf, handball, hockey, ... motion mainly plays on : ... (the trajectory of the projectile). We have tried

ITL Public School · 24 (a) What is projectile? Derive the expression for the trajectory, maximum height, time of flight, and horizontal range for a projectile thrown upward, making

Developing Planning and Controls for Highway Lane Change ... · (LCM) system for highway driving scenario (straight & curved roads) Generates a collision-free, optimal trajectory

Projectile motion - Amazon S3 · Projectile motion Objectives • Identify examples of projectile motion. • Solve projectile motion problems. problems • Graph the motion of a

The Optimum Launch Angle of a Projectile - · PDF fileUsing a marble and a curved ramp as a model of projectile motion, ... lowers the optimum launch angle of a projectile, ... affected

Projectile Motion > Projectile

Projectile motion The curved path that an object follows when thrown, launched, or otherwise projected near the surface of the Earth

Projectile Motion & Vectors. Projectile motion is the motion of an object in flight including the impact of gravity The curved flight of a football or

Chapter 3 Accelerationpleclair.ua.edu/ph125/Slides/L5-6-accel.pdf · •Model the vertical trajectory of projectiles as objects that are in free fall. •Represent projectile motion

Projectile motion. A projectile is an object in motion that is only affected by gravity. Projectiles travel in trajectories: smooth curved paths that

Kinematics: Projectile Motionscienceres-edcp-educ.sites.olt.ubc.ca/files/2015/... · Justification: The time of flight of a projectile depends entirely on the height of the trajectory

Projectile Motion 2012 1 Projectile 2013

Projectile Motion The motion of an object that is thrown and moves along a curved path through the influence of gravity, only

Projectile Motion. Objects in projectile motion follow a parabolic path called a trajectory

Projectile Motion Determined by the initial velocity, gravity, and air resistance. Footballs, baseballs … any projectile will follow this parabolic trajectory

Projectiles Motion in Two Dimensions Chapter 7. Projectile An object launched into the air by a force Trajectory The path followed by a projectile

Two-Dimensional Motion Chapter 3. A little vocab Projectile = any object that moves through space acted on only by gravity Trajectory = the path followed

jmccullough/HW/Chapter 3 Problems.pdf · If the trajectory of the projectile is near the earth's ... The drawing shows projectile motion at three points along the tra- jectory. The

Projectile Lab – student - Stanford Universityajspakow/downloads/outreach/projectile... · Projectile Lab – student You will shoot a projectile across the room using a rubber

ANALYSIS OF THE 155 MM ERFB/BB PROJECTILE TRAJECTORY …aimt.unob.cz/articles/06_01/06_01 (7).pdf · ANALYSIS OF THE 155 MM ERFB/BB PROJECTILE TRAJECTORY ... The article is focused

Projectile Motion - PhysLab · Figure 1: A diagram representing the trajectory of a projectile and di erent parameters associatedB with this kind of motion. which will connect the

WOTW: TRAJECTORY: noun - Oconomowoc Schools fileWOTW: TRAJECTORY: noun The path followed by a projectile flying or an object moving under the action of given forces. Or “a curve

Projectiles Objects that are thrown or launched into the air and are subject to gravity are called projectiles. Projectile motion is the curved path that

Physics Learning Achievement Study: Projectile, using … · University students who study projectile motion, using projectile motion experiment set at 0.01 level Keywords: projectile

Projectile Motion and Trajectory

Trajectory and Projectile Motion

Katholieke Hogeschool Limburg - Sisu@UT · PDF fileQuantum Spin Off 1 ... Predicting the trajectory of an horizontally launched projectile ... you will investigate whether this dual

ITL Public School · 26 a) What is projectile? Derive the expression for the trajectory, maximum height, time of flight, and horizontal range for a projectile thrown upward, making

Projectile Flight Trajectory and Position Estimation ... · flow is applied to the detection of moving objects from dynamic images, which utilizes the . 3484 Sensors and Materials,

Projectile Motion - fulmerphysics.weebly.com€¦ · What is Projectile Motion? Projectile Motion is a form of motion in which an object is thrown and follows a curved path under

Motion is Relative Straight Linear Falling Curved Circular/ Angular/ Rotational Projectile