Topic - • Calculus

VolsOfRevolution.htm
VolsOfRevolution.exe
VolsOfRevolution.mov

An animation of an arc on a grid where the arc is spun (lathed) on its X axis into a solid "bullet" shaped object. Then circular slices are highlighted, and one of them is then pulled from the object and spun around to show its shape. This introduces the topic of volumes of revolution.
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Vol_Using_Shells.htm
Vol_Using_Shells.exe
Vol_Using_Shells.mov

An animation of a parabola on a grid which is spun (lathed) on its Y axis to produce a "bundt cake" shaped half-donut. From this solid are highlighted rings, and one of the rings is pulled from the solid, opened up into a flat strip and spun around to show its shape. This introduces the topic of volume using the Shell method.
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PistonAnim.html or PistonAnim.exe
This animation demonstrates a related rate application over time using a piston. It can be started and stopped at any point in the cycle.
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BaseRunner.html or BaseRunner.exe
This animations depicts a rate of change topic using the runner's position relative to the home plate as he runs to third base.
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BaseRunner_and_ball.html or BaseRunner_and_ball.exe
This animations depicts a rate of change topic involving a baseball player trying to throw a runner out at 3rd base.
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BaseRunnerHome_and_2nd.html or
BaseRunnerHome_and_2nd.exe

This animations depicts a rate of change topic involving the distance between two base runners.
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Cylinder_In_a_Sphere.htm
Cylinder_In_a_Sphere.exe
Cylinder_In_a_Sphere.mov

An animation of a blue wireframe globe spinning in place. Inside is a semi-transparent cylinder that expands and shrinks from a tall slim cylinder to a large diameter but thin slice of a cylinder and back again, showing all the possible variations of size and volume of a cylinder within a given sphere (a Max/Min problem).
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Cylinder_in_Sphere.jpg and
Cylinder_in_Sphere_with_Labels.jpg
(used in conjunction with the adjacent "Cylinder in a Sphere" animation)
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Silos.htm or Silos.exe or Silos.mov
An animation showing different views of four silos of different heights and diameters, visualizing how the various parameters effect the size and volume of the dome-shaped top. This is used to introduce a problem involving calculating the most cost-effective construction of a silo to hold a given volume of grain. The silo's domed top cannot be used to store grain and its cost of construction per volume measurement is greater than the cylindrical portion, thus creating the need to get the most cylindrical volume vs. dome volume to reduce construction cost for a given storage volume. (a Max/Min problem)
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4_Silos_Front_View.jpg
One of several still images from the "Silos" animation, showing various views of four silos, making it easier to visually compare the relative shapes and sizes:
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4_Silos_High_View.jpg
One of several still images from the "Silos" animation, showing various views of four silos, making it easier to visually compare the relative shapes and sizes:
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4_Silos_Oblique_View.jpg
One of several still images from the "Silos" animation, showing various views of four silos, making it easier to visually compare the relative shapes and sizes:
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Silo_10x2.5.jpg
One of several still images from the "Silos" animation, showing various views of four silos, making it easier to visually compare the relative shapes and sizes:
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Silo_7.5x4.4.jpg
One of several still images from the "Silos" animation, showing various views of four silos, making it easier to visually compare the relative shapes and sizes:
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Silo_5x10.jpg
One of several still images from the "Silos" animation, showing various views of four silos, making it easier to visually compare the relative shapes and sizes:
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Silo_2.5x40.jpg
One of several still images from the "Silos" animation, showing various views of four silos, making it easier to visually compare the relative shapes and sizes:
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Silo_Transparent_ with_Labels.jpg
One of several still images from the "Silos" animation, showing various views of four silos, making it easier to visually compare the relative shapes and sizes:
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Silo_Transparent_no_Labels.jpg
One of several still images from the "Silos" animation, showing various views of four silos, making it easier to visually compare the relative shapes and sizes:
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CannonTrajectory.htm
CannonTrajectory.exe
CannonTrajectory.mov

CannonTrajectory_anim.gif

An animation showing the forces on a projectile at different points in the flight path. Used for Calculus in solving differential equations and also for Euler’s Method.
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Picture4.htm
Picture4.exe
Picture4.mov

An animation - girl viewing a painting on the wall. Painting is 3' high, the bottom edge of it hangs 4' above the girl’s eyelevel. Find distance X from the wall where the girls viewing angle is best.
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TreasureDig.htm
TreasureDig.exe
TreasureDig.mov

An animation - a pirate buries his treasure in the side of a mountian that is an island. Picturing the island as a parabola on a grid, calculate whether the shortest route to dig to the treasure is a vertical or horizontal tunnel.
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Skater.htm or Skater.exe
Skater.mov
or Skater_anim.gif

This animation shows an overhead view of an ice skater skating in an ellipse, which is superimposed on a coordinate plane. When the skater falls down, she slides off at a tangent to the ellipse (related rates problem).
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Tartown.htm or Tartown.exe
Tartown.mov
or Tartown_anim.gif

In this animation two friends are talking on cell phones, each traveling in a car, one headed into Tartown, and one headed out of Tartown on highways that are at right angles to each other. From this overhead view, calculate the rate at which their distance from each other is changing (related rates problem).
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Balloon.htm or Balloon.exe
Balloon.mov
or Balloon_anim.gif

An animation showing a hot air balloon going up vertically at 90 degrees.
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Balloon_70degrees.htm
Balloon_70degrees.exe
Balloon_70degrees.mov
Balloon_70degrees_anim.gif

An animation showing a hot air balloon going up vertically, but at a 70 degree angle to the ground.
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BoatPull.htm or BoatPull.exe
BoatPull.mov
or BoatPull_anim.gif

An animation. A man on a pier uses a rope to pull his rowboat closer to the pier. The rate of the boat’s approach changes with distance to the pier (related rates problem).
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Plane-n-Camera.htm
Plane-n-Camera.exe
Plane-n-Camera.mov
Plane-n-Camera_anim.gif

An animation showing a girl watching an approaching airplane through her video camera. The angle changes as the plane comes closer. (related rates problem)
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RugbyField.htm or RugbyField.exe
RugbyField.mov
or RugbyField_anim.gif

An animation. A player wants to find the optimum angle from the sideline to kick the ball into the goal so he has the widest possible target.
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