Deriving the Range Equation Or, how to get there from here.

Slides:

Advertisements

Similar presentations

PROJECTILE MOTION Free powerpoints at

Advertisements

Motion with Uniform Acceleration

7-2 Projectile Motion. Independence of Motion in 2-D Projectile is an object that has been given an intial thrust (ignore air resistance)  Football,

Motion in Two Dimensions

Projectile Motion Motion in two directions. What is a projectile? A projectile is an object upon which the only force acting is gravity. A projectile.

NON NON – POLY ATTIRE, ID’s AROUND YOUR NECK OBJECTIVE` Be able to solve the x and y components of a vector. Drill 2.10: Drill 2.10: trig functions Date:

Special Cases of Force Projectile Motion.

Projectile Motion.

Regents Physics – Mr. Rockensies

Part 2: projectiles launched at an angle Pages 102 – 104 Motion in Two Dimensions.

Unit 4 Class Notes Accelerated Physics Projectile Motion Days 1 thru 3.

Projectile Motion. What is a PROJECTILE? An object that is projected (launched) It continues in motion due to its own inertia, Is only acted upon by gravity.

Projectile Motion Type I Type II. Projectile Motion Any object that has been given an initial thrust, then moves only under the force of gravity. The.

Projectile Motion. Vocabulary 1.Resultant 2.Component 3.Resolution 4.Projectile 5.Trajectory -The path that the projectile follows 6.Range – pg 77.

Projectile Calculations Notes

Ideal Projectile Equations: If the only force is weight, then the x velocity stays constant (a x = 0). The y velocity changes with time and position (y.

Parabolic Motion Movement in two dimensions. Shape of the Motion The motion is parabolic in shape:

Warm Up 1. g = _________ 1. g = _________ Don’t forget units* Don’t forget units* 2. True or False: In a Vacuum Heavy objects fall faster than less massive.

Lecture 5: Vectors & Motion in 2 Dimensions. Questions of Yesterday 2) I drop ball A and it hits the ground at t 1. I throw ball B horizontally (v 0y.

Projectile Motion: Questions to Ponder What are the three factors that will determine how far an object will travel when thrown? What are the two things.

Projectile Motion Horizontally Launched Projectiles Projectiles Launched at an Angle A.S – Due Friday, 11/14 Text Reference: chapter 3.

Physics pre-AP. Equations of motion : We assume NO AIR RESISTANCE! (Welcome to “Physicsland”), therefore… The path of a projectile is a parabola. Horizontal.

MOTION OF A PROJECTILE Today’s Objectives: Students will be able to: 1.Analyze the free-flight motion of a projectile. In-Class Activities: Check Homework.

Projectile Motion Projectiles launched at an angle.

Introduction to Projectile Motion

2-Dimensional Kinematics Unit 2 Presentation 2. Projectile Problems  Projectile Motion: The two- dimensional (x and y) motion of an object through space.

Projectiles calculations Calculating the components of a vector using trigonometry and vertical and horizontal problems.

Projectile motion.

Motion of Projectiles. An object that has projectile motion has an initial velocity, follows a curved path(trajectory) and reaches the ground due to the.

Projectile Motion-Starter What is the path that the bike and the water take called?

Physics Lesson 6 Projectile Motion Eleanor Roosevelt High School Mr. Chin-Sung Lin.

Projectile Motion.

Objectives: Analyze the motion of an object in free fall. Solve two-dimensional problems. Calculate the range of a projectile.

Physics Lesson 6 Projectile Motion

Derivation of the proportionality of velocity and radius for an object in circular motion under a constant centripetal force.

Two-Dimensional Motion. One-Dimensional Motion An object moving only in one direction, either in x-direction OR y- direction. An object moving only in.

Unit 6 Notes. Free-Fall: When an object is flying through the air and the only force acting on it is gravity. In our mini-lab with the cannons, we analyzed.

Motion in Two Dimensions

Angled Projectiles. Projectiles an angle These projectiles are different from those launched horizontally since they now have an initial vertical.

MOTION OF A PROJECTILE Today’s Objectives: Students will be able to: 1.Analyze the free-flight motion of a projectile. In-Class Activities: Check Homework.

Motion in One Direction Chapter 2 Goals: motion, displacement, velocity, acceleration, freefall, acceleration due to gravity and equations to solve for.

 Vectors are quantities with Magnitude AND Direction  Ex: › Displacement › Velocity › Acceleration › Force  Scalars are quantities with only magnitude.

Motion in Two Dimensions Chapter 7.2 Projectile Motion What is the path of a projectile as it moves through the air? ? . What forces act on projectiles?

Notes: Projectile Motion. Projectiles are... Objects thrown or launched into the air Objects thrown or launched into the air While in the air, gravity.

For each diagram below, create a free diagram of the ball at the top of the path As you view the following video and animation think about the forces.

Motion in Two Dimensions

Copyright © 2010 Pearson Education, Inc. Chapter 4 Two-Dimensional Kinematics.

(a) 1, (b) 3 Fig. 4-6, shows the direction of acceleration for a particle located at its tail, and its length (representing the acceleration.

Projectile Motion The motion of a falling object with air resistance and gravity acting on it.

Projectile Motion. Horizontally Launched Projectiles Projectiles which have NO upward trajectory and NO initial VERTICAL velocity. Y-Direction Free Fall.

Acceleration Acceleration is the rate of change of velocity.

Projectile Motion Projectiles The Range Equation.

Two dimensional motion: PROJECTILE MOTION

Motion in Two and Three Dimensions Chapter 4. Position and Displacement A position vector locates a particle in space o Extends from a reference point.

Introduction to 2D Projectile Motion Types of Projectiles Which one is NOT a projectile?

Projectiles IB Revision. Gravity does not act sideways gravity makes it accelerate downwards The ball moves with a constant horizontal velocity The ball.

What is Projectile Motion?. Instructional Objectives: Students will be able to: –Define Projectile Motion –Distinguish between the different types of.

Physics Lesson 6 Projectile Motion

Lesson 3: Physics 150 / 215 Projectile Motion

PROJECTILE MOTION.

Projectile Motion Part 2.

Projectile Motion.

Projectile Motion.

Projectile Motion A projectile is an object moving in two or three dimensions only under the influence of gravity.

Angled Projectiles.

Topic 9.2 Space Projectile Motion.

Projectile Motion and Relative Velocity

Presentation transcript:

Deriving the Range Equation Or, how to get there from here

Keep in mind... Horizontal velocity REMAINS CONSTANT – No net force is acting horizontally so there is no horizontal acceleration Vertical velocity CHANGES – Acceleration due to gravity, ~9.81 m/s 2 – Caused by the unbalanced force of gravity acting on the object

y max x x R = 2x

y max x x R = 2x  vivi

 vivi v iy = v i sin  v x = v i cos 

y max x x R = 2x  vivi v iy = v i sin  v x =v i cos 

y max x x R = 2x  vivi

y max x x R = 2x  vivi At the top of the path, v fy = 0

y max x x R = 2x  vivi Substituting in

y max x x R = 2x  vivi Substituting in

 vivi v iy = v i sin  v x = v i cos  Remember that the initial velocity in the y-direction = v i sin 

y max x x R = 2x  vivi

The whole point here is to solve for x...

Remember that the range, R, = 2x