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
Visualizing, adding and breaking down vectors in 2 dimensions
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Projectile at an angle
Figuring out the horizontal displacement for a projectile launched at an angle
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Different way to determine time in air
Another way to determine time in the air given an initial vertical velocity
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Launching and landing on different elevations
More complicated example involving launching and landing at different elevations
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Total displacement for projectile
Reconstructing the total displacement vector for a projectile
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Total final velocity for projectile
Calculating 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
Correction to "Total Final Velocity for Projectile" Video
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Projectile on an incline
Challenging problem of a projectile on an inclined plane
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Unit vectors and engineering notation
Using unit vectors to represent the components of a vector
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Unit vector notation
Expressing a vector as the scaled sum of unit vectors
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Unit vector notation (part 2)
More 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
Solving 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
Optimal 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)
Horizontal 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
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
When acceleration could involve a change in direction and not speed
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Centripetal force and acceleration intuition
The direction of the force in cases of circular motion at constant speeds
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Visual understanding of centripetal acceleration formula
Visual understanding of how centripetal acceleration relates to velocity and radius
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Optimal turns at Indianapolis Motor Speedway with JR Hildebrand
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Calculus proof of centripetal acceleration formula
Proving that a = v^2/r
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Loop de loop question
Asks students to find the minimum speed necessary to complete the loop de loop
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Loop de loop answer part 1
Figuring 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
Figuring 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 your mind around this super-fun topic.