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mes
MES Science
2M
Vector Functions: Problems Plus
Vector Functions: Problems Plus
49.138809, -123.108071
Five hour deep-dive into 7 advanced math problems on vector functions. Buckle up!
408
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mes
SciFi Multiverse
1M
Problems Plus 6: Cable wound around a spool
Problems Plus 6: Cable wound around a spool
In this video, I calculate the height covered by a coil of cable of known length around a spool, counting only the portion of the height that includes a full loop. Notes - 3Speak #math #calculus #physics
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mes
MES Science
1M
Problems Plus 6: Cable wound around a spool
Problems Plus 6: Cable wound around a spool
Deep dive into deriving an equation for the height covered by a cable wound around a spool, for any given cable thickness or spool radius.
mes
SciFi Multiverse
1M
Problems Plus 5: Launch Angle of 56° maximizes TOTAL distance a projectile travels
Problems Plus 5: Launch Angle of 56° maximizes TOTAL distance a projectile travels
In this video, I show that firing a projectile has a maximum total distance traveled in the air when the launch angle is approximately 56°. This is 11° higher than the 45° angle needed to maximize the
mes
MES Science
1M
Problems Plus 5: Launch Angle of 56° maximizes TOTAL distance a projectile travels
Problems Plus 5: Launch Angle of 56° maximizes TOTAL distance a projectile travels
Extensive tutorial on deriving the launch angle to maximize the total distance, not just horizontal distance, that a projectile travels in the air.
mes
SciFi Multiverse
1M
Problems Plus 4: Curvature from Parametric Equations that involve Integrals
Problems Plus 4: Curvature from Parametric Equations that involve Integrals
In this video, I show how to obtain the curvature of parametric equations that involve integrals, by first utilizing the fundamental theorem of calculus to obtain the derivative of the position vector
mes
MES Science
1M
Problems Plus 4: Curvature from Parametric Equations that involve Integrals
Problems Plus 4: Curvature from Parametric Equations that involve Integrals
The curvature of a space curve is obtained when given its parametric equations as integrals for the x and y components.
mes
SciFi Multiverse
1M
Problems Plus 3: Physics of a Ball Rolling Off a Table
Problems Plus 3: Physics of a Ball Rolling Off a Table
In this video, I go over the physics of a ball rolling off a table and determine how far it falls, the angle and speed it bounces with, and the distance it travels for a second bounce after losing 80%
mes
MES Science
1M
Problems Plus 3: Physics of a Ball Rolling Off a Table
Problems Plus 3: Physics of a Ball Rolling Off a Table
The physics of a ball rolling off of a table is explained via vector functions and vector calculus.
mes
MES Science
2M
Problems Plus 2: Firing a Projectile Up and Down an Inclined Plane
Problems Plus 2: Firing a Projectile Up and Down an Inclined Plane
In this video, I go over projectile motion along an inclined plane and show that the launch angle that gives the maximum range upwards or downwards is half the angle between the plane and the vertical.
mes
MES Science
2M
Problems Plus 2: Firing a Projectile Up and Down an Inclined Plane
Problems Plus 2: Firing a Projectile Up and Down an Inclined Plane
Firing a projectile up or down an inclined plane goes the furthest when the launch angle is half the angle between the plane and the vertical!
mes
SciFi Multiverse
2M
Projectile aimed at a target downrange will always hit when dropped and fired at the same time!
Projectile aimed at a target downrange will always hit when dropped and fired at the same time!
In this video, I show that firing a projectile while aiming at a distance target downrange and dropping it at the same time will always cause the projectile to hit the target, provided that the projectile
mes
MES Science
2M
Projectile aimed at a target downrange will always hit when dropped and fired at the same time!
Projectile aimed at a target downrange will always hit when dropped and fired at the same time!
The math checks out: aiming at a distant target and then firing a projectile at the same time as dropping the target will always hit!
mes
SciFi Multiverse
2M
Problems Plus 1: Projectile fired from the origin
Problems Plus 1: Projectile fired from the origin
In this video, I examine projectile motion launched from the origin and show that the projectile will always lie within a parabola defined by launching a projectile from the maximum height horizontally
mes
MES Science
2M
Problems Plus 1: Projectile fired from the origin
Problems Plus 1: Projectile fired from the origin
Analyzing projectile motion of an object launched from the origin and analyzing its maximum height, flight path, and ability to hit distant targets.
mes
SciFi Multiverse
2M
Vector Functions: Problems Plus
Vector Functions: Problems Plus
In this video, I go over the end-of-chapter Problems Plus questions and solve 7 very advanced problems on vector functions. Three of the questions involve launching a projectile either on a flat, inclined,
mes
SciFi Multiverse
3M
Review of Vector Functions – True-False Quiz
Review of Vector Functions – True-False Quiz
In this video, I go over the True-False Quiz at the end of the chapter on vector functions from my calculus book. There are 14 questions, and I cover vector equations of lines, parabolas, differentiation,
mes
MES Science
3M
Review of Vector Functions – True-False Quiz
Review of Vector Functions – True-False Quiz
I go over the solutions of the true-false quiz at the end of my calculus book chapter on Vector Functions.
mes
SciFi Multiverse
4M
Vector Equation of a Tangent Line on a Space Curve
Vector Equation of a Tangent Line on a Space Curve
In this video, I go through obtaining the vector equation of a tangent line to a space curve, by replacing the parallel vector with the tangent vector from the general vector equation of a line. This was
mes
MES Science
4M
Vector Equation of a Tangent Line on a Space Curve
Vector Equation of a Tangent Line on a Space Curve
Tutorial on obtaining the tangent vector, unit tangent vector, and equation of the tangent line to a space curve.

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