Khan Academy on a Stick
Two-dimensional motion
You understand velocity and acceleration well in one-dimension. Now we can explore scenarios that are even more fun. With a little bit of trigonometry (you might want to review your basic trig, especially what sin and cos are), we can think about whether a baseball can clear the "green monster" at Fenway Park.
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Visualizing Vectors in 2 Dimensions
ccVisualizing, adding and breaking down vectors in 2 dimensions
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Projectile at an Angle
ccFiguring out the horizontal displacement for a projectile launched at an angle
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Different Way to Determine Time in Air
ccAnother way to determine time in the air given an initial vertical velocity
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Launching and Landing on Different Elevations
ccMore complicated example involving launching and landing at different elevations
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Total Displacement for Projectile
ccReconstructing the total displacement vector for a projectile
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Total Final Velocity for Projectile
ccCalculating the total final velocity for a projectile landing at a different altitude (mistake near end: I write 29.03 when it should be 26.03 m/s and the final total magnitude should be 26.55 m/s 78.7 degrees below horizontal
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Correction to Total Final Velocity for Projectile
ccCorrection to "Total Final Velocity for Projectile" Video
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Projectile on an Incline
ccChallenging problem of a projectile on an inclined plane
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Unit Vectors and Engineering Notation
ccUsing unit vectors to represent the components of a vector
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Clearing the Green Monster at Fenway
ccSetting up the problem to determine the minimum velocity to hit a ball with to clear the Green Monster
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Green Monster at Fenway Part 2
ccSolving the problem to determine the minimum velocity to hit a ball with to clear the Green Monster
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Unit Vector Notation
ccExpressing a vector as the scaled sum of unit vectors
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Unit Vector Notation (part 2)
ccMore on unit vector notation. Showing that adding the x and y components of two vectors is equivalent to adding the vectors visually using the head-to-tail method
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Projectile Motion with Ordered Set Notation
ccSolving the second part to the projectile motion problem (with wind gust) using ordered set vector notation
Two-dimensional projectile motion
Let's escape from the binds of one-dimension (where we were forced to launch things straight up) and start launching at angles. With a little bit of trig (might want to review sin and cos) we'll be figuring out just how long and far something can travel.
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Optimal angle for a projectile part 1
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Optimal angle for a projectile part 2 - Hangtime
ccOptimal angle for a projectile part 2 - Hangtime
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Optimal angle for a projectile part 3 - Horizontal distance as a function of angle (and speed)
ccHorizontal distance as a function of angle (and speed)
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Optimal angle for a projectile part 4 Finding the optimal angle and distance with a bit of calculus
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Optimal angle for a projectile
This tutorial tackles a fundamental question when trying to launch things as far as possible (key if you're looking to capture a fort with anything from water balloons to arrows). With a bit of calculus, we'll get to a fairly intuitive answer.
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Race Cars with Constant Speed Around Curve
ccWhen acceleration could involve a change in direction and not speed
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Centripetal Force and Acceleration Intuition
ccThe direction of the force in cases of circular motion at constant speeds
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Visual Understanding of Centripetal Acceleration Formula
ccVisual understanding of how centripetal acceleration relates to velocity and radius
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Calculus proof of centripetal acceleration formula
ccProving that a = v^2/r
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Loop De Loop Question
ccAsks students to find the minimum speed necessary to complete the loop de loop
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Loop De Loop Answer part 1
ccFiguring out the minimum speed at the top of the loop de loop to stay on the track
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Loop De Loop Answer part 2
ccFiguring out the car's average speed while completing the loop de loop
Centripetal acceleration
Why do things move in circles? Seriously. Why does *anything* ever move in a circle (straight lines seem much more natural). ? Is something moving in a circle at a constant speed accelerating? If so, in what direction? This tutorial will help you get mind around this super-fun topic.