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mes
MES Science
1M
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
3
mes
SciFi Multiverse
7d
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
55
mes
MES Science
11d
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
14d
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
17d
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
21d
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
21d
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
24d
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
24d
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
1M
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
SciFi Multiverse
1M
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
1M
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
1M
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
SciFi Multiverse
1M
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
MES Science
5M
Tangential and Normal Components of Acceleration
Tangential and Normal Components of Acceleration
In this video, I write the vector equation of acceleration in terms of its unit tangent and unit normal vector components, which is useful when analyzing the motion of a particle along a curve. The unit
mes
SciFi Multiverse
6M
Example 3: Integrating Acceleration and Velocity Vectors to get the Position Vector
Example 3: Integrating Acceleration and Velocity Vectors to get the Position Vector
In this video, I show that we can obtain the velocity of a moving object by first integrating its acceleration vector to obtain its velocity and then integrating the velocity vector. This follows from
mes
SciFi Multiverse
6M
Motion in Space: Velocity and Acceleration
Motion in Space: Velocity and Acceleration
In this video, I go over further into vector functions, and this time look at motion in space in terms of the velocity, acceleration, and position of objects moving in 2D or 3D space. Using the fact that
mes
MES Science
6M
Motion in Space: Velocity and Acceleration
Motion in Space: Velocity and Acceleration
49.138916, -123.108144
In this video, I go over further into vector functions, and this time look at motion in space in terms of the velocity, acceleration, and position of objects moving in 2D or 3D space. Using the fact that
mes
SciFi Multiverse
9M
Osculating Circle of a Parabola + Summary of TNB Vectors and Curvature Formulas
Osculating Circle of a Parabola + Summary of TNB Vectors and Curvature Formulas
In this video, I go over the osculating circle, which lies on the same osculating plane and has the same tangent and normal vector as a given point on a space curve. I illustrate this by determining the
mes
MES Science
9M
Normal and Binormal Vectors + Example on a Circular Helix
Normal and Binormal Vectors + Example on a Circular Helix
In this video, I go over the principal unit normal and binormal vectors of a space curve, which are both derived from the unit tangent vector. Since the unit tangent vector is a constant-length one, its

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