Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved...

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Projectile Motion

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Transcript of Projectile Motion. What is a Projectile? Projectile – an object that moves along a 2-D curved...

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.

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

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

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

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

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

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

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

1 Non Linear Motion 2 Definitions: projectile - An object that is thrown,tossed, or launched. trajectory - The pathway of a projectile. Usually follows.

1 Non Linear Motion 2 Definitions: projectile - An object that is thrown,tossed, or launched. trajectory - The pathway of a projectile. Usually follows.

Projectile Motion Projectile HW #1: Handout. Projectile Motion: Introduction: Projectile motion refers to freefall motion in ______ dimensions. The motion.

Projectile Motion Projectile HW #1: Handout. Projectile Motion: Introduction: Projectile motion refers to freefall motion in ______ dimensions. The motion.

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

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.

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 and Trajectory

Projectile Motion and Trajectory

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

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

Projectile Motion 2012 1 Projectile 2013

Projectile Motion 2012 1 Projectile 2013

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

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

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

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

Projectile Motion Chapter 3. Vector and Scalar Quantities Nonlinear Motion: motion along a curved path. Magnitude: greatness in size or extent. Vector.

Projectile Motion Chapter 3. Vector and Scalar Quantities Nonlinear Motion: motion along a curved path. Magnitude: greatness in size or extent. Vector.

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

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

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

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

The Influence of Projectile Trajectory Angle on the ...

The Influence of Projectile Trajectory Angle on the ...

Projectile Motion > Projectile

Projectile Motion > Projectile

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

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

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

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