12.3 Velocity and Acceleration. Projectile Motion.

Slides:

Advertisements

Similar presentations

Tangent Vectors and Normal Vectors. Definitions of Unit Tangent Vector.

Advertisements

 Find an equation of the tangent line to the curve at the point (2, 1).

PLAY Physics Con-Seal From RegentsEarth.com.

Projectile Motion.

Projectile Motion Neglecting air resistance, what happens when you throw a ball up from the back of a moving truck? Front? Behind? In?

Lesson Thread I Full Projectile Motion 12/1/20131Intellectual Property of Mr. Gary.

5.6 Projectiles Launched at an Angle

Parametric Equations Day 2 TS: Examining Information from more than one viewpoint Warm Up: Eliminate the parameter and then sketch the graph. Do not forget.

Particle Kinematics: Intro to Curvilinear Motion Current unit: Particle Kinematics Last two classes: Straight Line Motion Today: (a) Intro to Curvilinear.

PH 201 Dr. Cecilia Vogel Lecture 4. REVIEW  Constant acceleration  x vs t, v vs t, v vs x  Vectors  notation  magnitude and direction OUTLINE  2-D.

Lecture III Curvilinear Motion.

Projectile Motion Physics 6A Prepared by Vince Zaccone

Velocity and Acceleration. Definitions of Velocity and Acceleration.

Vector-Valued Functions Copyright © Cengage Learning. All rights reserved.

Precalculus Pre-AP SUMMER Defining a Function  When defining a function, we use coordinate points… ( x, y )  Typically, we use “x” to find out.

Projectile Motion Neglecting air resistance, what happens when you throw a ball up from the back of a moving truck? Front? Behind? In? GBS Physics Demo.

What is Projectile Motion?

Projectile Motion Projectile motion: a combination of horizontal motion with constant horizontal velocity and vertical motion with a constant downward.

Warm UpMay 8 th 1) Determine whether or not (104, -200) is a point on the graph of x = 4 + t, y = t. 2) Imagine you are piloting a small plane at.

10 extra topic: Projectile Motion Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002 Fort Pulaski, GA.

Vectors and Parametric Equations

1 Chapter 6: Motion in a Plane. 2 Position and Velocity in 2-D Displacement Velocity Average velocity Instantaneous velocity Instantaneous acceleration.

Vector-Valued Functions 12 Copyright © Cengage Learning. All rights reserved.

Today in Precalculus Go over homework Notes: Simulating Projectile Motion Homework.

Chapter-3 Falling Objects and Projectile Motion

Physics Lesson 6 Projectile Motion

6.3 Parametric Equations and Motion

10.6 Plane Curves and Parametric Equations. Let x = f(t) and y = g(t), where f and g are two functions whose common domain is some interval I. The collection.

Sullivan Algebra and Trigonometry: Section 11.7 Objectives of this Section Graph Parametric Equations Find a Rectangular Equation for a Curve Defined Parametrically.

10.4 Projectile Motion Fort Pulaski, GA. One early use of calculus was to study projectile motion. In this section we assume ideal projectile motion:

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

Sticky Ball Review Game Vectors and Parametrics (6.1, 6.3)

Chapter 3 Kinematics in Two Dimensions. 3.1 – d, v, & a A bullet is fired horizontally. A second bullet is dropped at the same time and at from the same.

CHAPTER 6 MOTION IN 2 DIMENSIONS.

Quadratics Review y = x 2. Quadratics Review This graph opens upwards y = x 2.

12 Vector-Valued Functions

Projectile Motion. Horizontal (x)Vertical (y) tt Projectile Motion Simulator.

A baseball is hit from an initial height of 1m. 8 seconds later, a fielder who is 25m away catches the ball at a height of 1m. What is the initial velocity.

Projectiles o A golf ball is hit with a speed of 50ms -1 at an elevation of 40 o along a level course.

Arc Length and Curvature

Vector Functions A vector function is a vector whose components are real-valued functions of a common variable (parameter), usually t.  We’ve seen a vector.

Projectile Motion Introduction Horizontal launch.

Mechanics 5 Applying the SUVAT equations to solve problems in one and in two dimensions IFP 6th November 2015.

(Constant acceleration)

Vector-Valued Functions and Motion in Space

Projectile Review.

Review Questions Chapter 3

Find the derivative of the vector function r(t) = {image}

9.8: Modeling Motion Using Parametric Equations

Projectile Motion.

Find the velocity of a particle with the given position function

y = B t - 1, x = t - 9 are the parametric equations of the curve

12.4 Tangent Vectors and Normal Vectors

9-4 Quadratic Equations and Projectiles

Projectile motion Projectile Motion Subject to Gravity Assumptions:

Tangent and Normal Vectors

PROJECTILE MOTION Thrown objects do not travel in a straight line. They tend to curve downward. Anything that is thrown or shot through the air is a.

Bellringer What is the difference between the words vertical and horizontal? What does the word projectile mean? How is one dimensional (1D), two dimensional.

Physics Support Materials Higher Mechanics and Properties of Matter

A projectile launched at an angle

Chapter 3 Jeopardy Review

y = C t - 1, x = t - 6 are the parametric equations of the curve

9.8: Modeling Motion Using Parametric Equations

What is Projectile Motion?

12.5: Vector PVA.

10.7 Parametric Equations parametric equations: a pair of equations, one for x and one for y, relating both to a third variable t.

Projectile motion.

12 Vector-Valued Functions

In the previous chapter we studied simple straight-line motion—linear motion.

Click to see each answer.

Presentation transcript:

12.3 Velocity and Acceleration

Projectile Motion

Examples A baseball player at second base throws a ball 90 feet to the player at first base. The ball is thrown at 50 miles per hour at an angle of 15 above the horizontal. At what height does the player at first base catch the ball if the ball is thrown from a height of 5 feet? A projectile is fired from ground level at an angle of 12 with the horizontal. Find the minimum initial velocity if the projectile is to have a range of 150 feet.

12.4 Tangent Vectors and Normal Vectors

Examples: 1)Find the unit tangent vector and find a set of parametric equations for the line tangent to the space curve at the point P. 2)Find the principal unit normal vector to the curve above at the specified point.

Sometimes shortcut to principal unit normal vector. For plane curves, you can find the principal unit normal vector by finding T(t)= and then observe that N(t) will either be OR It will be the one that points toward the concave side of the curve.

Examples: 1)Find T(t), N(t), and at the given time for the given curve r(t) r(t)= at t=1 r(t)= t=0