Motion in Two Dimensions

 

Projectile Motion

Equations for ballistic motion in two dimensions. Includes examples.

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Speed and acceleration at the apex of projectile's path. Solution not included.

Motion of a fielder running to catch a softball.

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Motion of a rock thrown upward from a bridge.

Motion of a ball projected upwards and at an angle.

Flight of a baseball.

Motion of an object that slides off the top step of a staircase.

3-part projectile motion problem involving stones thrown into the air.

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Vectors

Definition of a vector, displacement.

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Vector Operations

Addition, subtraction, negative of a vector; multiplying scalars and vectors.

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Vector Components

Components of vectors in two or three dimensions, with examples; unit vectors; arbitrary vector in terms of unit vectors example.

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Vector Multiplication

Definition of dot product, with example; distributive law.

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Cross Products

Definition of cross product of two vectors; right-hand rule; 2nd and 3rd order determinants; cross product examples.

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Motion in Three Dimensions

Extension of one-dimensional motion to three dimensions. Includes average and instantaneous velocity, average and instantaneous acceleration, and constant acceleration.

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Projectile Problem - Solving Strategy

List of steps for solving projectile motion problems in two-dimensions. Includes example.

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Circular Motion

Uniform circular motion; centripetal acceleration; non-uniform circular motion; reference frames; relativity of motion; problem-solving strategy for relative velocities with examples.

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Coordinate Systems

Overview of rectangular, spherical, and cylindrical coordinate systems.

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Vector Example Problem

Performing vector addition using vector components; vector component notation.

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Multi-Dimensional Kinematics

Velocity and acceleration in multiple dimensions; special case of projectile motion; solving quadratic equations.

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Projectile and Circular Motion

Projectile motion equations; circular motion equations; centripetal acceleration, with equation; dimensional analysis method.

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Two Dimensional Motion

Vector description of motion, including equations for position, velocity and acceleration; projectile motion; kinematic equations of motion in terms of x- and y- components; initial conditions; orbit equation with derivation.

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Experiment 2

Projectile motion experiment set-up and procedure.

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Indoor Cannon

3-part problem; maximizing distance for cannon to shoot when constrained by ceiling.

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Force Vector Addition

Determining what conditions must apply for force vectors to add up to zero. Solution not included.

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Kinematics in Two Dimensions

Velocity and acceleration of projectile motion. Solution not included.

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Throwing a Stone Down a Hill

Finding the landing point of a projectile on an inclined plane.

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Hitting the Bucket

Hitting a falling body with a projectile.

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Law of Addition of Velocities

Velocities in relatively inertial reference frames.

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Gravitational Slingshot

Acceleration in relatively inertial reference frames.

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Roller-coaster

Speed and acceleration of a cart on a roller-coaster. Solution not included.

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Two Projectiles

Projectile motion of two objects. Solution not included.

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Parabolic Orbit

Magnitude and direction of velocity for a parabolic orbit. Solution not included.

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Projectile and Falling Person

Motion of a stone thrown at a falling person. Solution not included.

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Second Law and Projectile Motion

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Motion of an object sliding off an inclined roof and falling to the ground.

Motion of an object sliding off an inclined roof and falling to the ground.

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Surveillance Balloon

3-part projectile problem; finding time and height of bullet hitting balloon, and time before firing (at fixed v, θ). Solutions are given at the end of each problem.

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Crossing a River

For boat crossing a flowing river, finding angle for direct crossing and for optimal time. Solutions are given at the end of each problem.

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Two Walkers

3-part 2D kinematics; finding point where walkers on square meet, distance to (0,0), and average velocity. Solutions are given at the end of each problem.

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Bomb Targeting

4-part problem; finding time and distance to impact, speed and location of impact. Solutions are given at the end of each problem.

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Reference Frames

Motion of a rock thrown from a bridge as seen from multiple reference frames.

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Motion of a thrown ball as seen by observers at different reference frames.

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Velocity and Acceleration

Finding and plotting the velocity and acceleration of a particle given equations for its position.

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Ball and Boat

Motion of a ball thrown from a moving boat.

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Collision of Two Projectiles

Motion of an acrobat catching a ball in mid-air.

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Different Punt Angles

Comparing distance and hangtime for a punt at two different angles.

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Addition of Velocities

Motion of a boat rowing across a river perpendicular to the current.

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