The following are my notes and animations on related
rates problems involving baseball. Note we can also use this format
for related rate problems involving planes, boats, and cars traveling on different bearings
Notes  Related Rates A Baseball Example
Animation3rd Base
Animation2d Base
Optimization
The following are my notes and animation on the optimization
problem a bird flies home.
Notes  A Bird Flies Home
AnimationA bird flies home
The following notes and animations deal with projectile
motion. The notes solve the problem of what firing angle maximizes
the range of a projectile fired from ground level. We first solve
the problem if the projectile is fired on flat ground. The seond deals with firing the projectile up a ramp. The animations correspond to these 2 situations.
Notes  Maximizing the Range of a Projectile
Animation  Projectile Fired on Level Ground
Animation  Projectile Fired up a Ramp
The following notes and animation deal with minimizing the
distance from a point to an ellipse.
NotesMinimizing the distance from a point to an ellipse
AnimationMinimum distance from a point to an ellipse
The following notes and animations use the product rule to find the maximum and minimum
heights of a mass on a spring where air resistance decreases the amplitudethis is known as the damped harmonic oscillator.
Max and Min Values of a Damped Mass on a Spring
AnimationNo Damping
AnimationDamped Motion
Minimization of Area
Let y1(x) = a3x2  a4x and y2(x) = x a.
Find the value of a minimizes the area b. What is the minimum area? 
Solution to Area Minimization Problem
Find the minimum area of the triangle formed by the tangent line to f(x) = x2 +2 at (a,f(a)),
the x axis and the line segment from the point (a,f(a))
to the point (4,0)
For 0 < a < 4 See the Animation Triangle 
Animation Triangle
Solution to Triangle Problem
