Ship Traveling in a Current

Description: The animation displays a ship traveling over the ocean. The animation also displays a bottle drifting with the ocean current (the bottle is only shown when the speed of the ocean current is not equal to zero. The animation can also be used to show the ship's path, ship's position vector, the polar coordinates of the ship, and the velocity vectors of both the ship and bottle (the animation does not yet show the addition of these velocity vectors). The animation can be used to learn about position vectors, Polar versus Cartesian coordinates, velocity vectors, vector addition using position vectors, and vector addition using velocity vectors.

Instructions:

1. Controlling the velocity of the ocean current:
1. The speed of the ocean current can be controlled by dragging the red triangle on the speedometer in the lower right hand side of the animation. The bottle, drifting along with the ocean current, will be visible only when the speed of the current is not equal to zero.
2. The direction of the velocity of the ocean current can be controlled by dragging the red needle of the compass on the right hand side of the animation.
3. You must first press stop in order to change the ocean current's speed and direction. Press play in order to resume the animation.
4. Press rewind in order to reset the animation to its initial conditions.
2. Controlling the velocity of the ship:
1. The speed of the ship can be controlled by dragging the purple triangle on the speedometer in the lower right hand side of the animation. To be more specific, the speedometer sets the speed of the ship relative to the water.
2. The direction of the velocity of the ship can be controlled by dragging the purple needle of the compass on the right hand side of the animation. To be more specific, the purple needle on the compass sets the direction of the velocity of the ship relative to the water.
3. You must first press stop in order to change the ship's speed and direction. Press play in order to resume the animation.
4. Press rewind in order to reset the animation to its initial conditions.
3. Displaying properties of the motion of the ship and ocean current:
1. Click on the appropriate check boxes in order to display the ship's position vector, the ship's path, the ship's Polar Coordinates, and the velocities of the ship and ocean current.
2. The ship's Cartesian Coordinates is indicated by the purple segments appearing on the x and y axes.
3. The white segments on the x and y axis' provide the Cartesian Coordinates of the cursor. This allows to find the Cartesian Coordinates of any point on the animation. For example, placing your mouse over the center of the coral reef shows that the Cartesian Coordinates of the center of the coral reef are (6,21).
4. Displaying on Polar Coordinates will also cause the position vector of the ship to be displayed. Conversely, turning off the position vector of the ship will also cause the Polar Coordinates of the ship to be turned off. The Polar Coordinates will not be displayed if the ship is too close to the origin and the angular coordinate will not be displayed if the position vector is to close to the x axis.
5. Three velocity vector will be displayed when the "velocity vector box is checked", namely the velocity of the bottle, the velocity of the ship relative to the water, and the velocity of the ship relative to land.
1. The bottle's velocity is identical to the velocity of the ocean current and determined by the compass and speedometer settings of the ocean current.
2. The ship's velocity relative to the water is displayed as a lavender, dashed vector and is one of two velocity vectors that is located coincidentally with the ship. The ship's velocity relative to the water is determined by the compass and speedometer settings of the ocean current.
3. The ship's velocity relative to the land is displayed as a green, dashed vector and is the second of two velocity vectors that is located coincidentally with the ship. The ship's velocity relative to the land is determined by adding the velocity of the ocean current to the ship's velocity relative to the water.

1. What are the Cartesian Coordinates of Questown, Anscoise, and the coral reef? Find the solution by placing your mouse over points A, B, and C, respectively (the white line segments on the x and y axis' provide you with the x and y coordinates of the mouse).
2. The ship travels due east (the x axis points due east) at a speed of 10 km/hour for 30 minutes. The ship then stops and turns due north and travels for 45 minutes at a speed of 20 km/hour. What are the x and y coordinates of the ship (the purple line segments on the x and y axis' provide you with the x and y coordinates of the ship) at this point in time? You will need to click on stop in order to change the ship's speed and heading.
3. What are the Cartesian Coordinates of the southern most tip of the coral reef? What are the Cartesian Coordinates of the northern most tip of the coral reef? What are the Cartesian Coordinates of the eastern most point of the coral reef? What is the x coordinate of the points along the western edge of the reef?
4. The ship sails due north at a speed of 10 km/hour for a period of 36 minutes. The ship then turns due east and travels for a period of 30 minutes at a speed of 30 km/hour. Did the ship strike the reef during the course of its journey? If so, then when did it strike the reef? If not, then were is the ship located, relative to the reef, at the end of its journey (i.e., how far away is the ship from the reef and is the ship north of the reef, northeast of the reef, east of the reef, etc.)? You will need to click on stop in order to change the ship's speed and heading.
5. The ship sails due east at a speed of 30 km/hour for a period of 54 minutes. The ship then turns due north and travels for a period of 24 minutes at the same speed. What are the Cartesian Coordinates of the ship? State the ship's position relative to the nearest landmark (i.e., relative to the reef, Anscoise, or Questown) You will need to click on stop in order to change the ship's speed and heading.
6. The ship is traveling at a speed of 30 km/hour due east. The ocean current (whose speed is controlled by the sliding red triangle on the "speedometer" and whose direction is controlled by the red compass needle) is moving at a speed of 10 km/hour in the northwardly direction. Will the ship strike the reef? The bottle in the animation drifts with the current.
7. The ship travels due north at a speed of 20 km/hour. The ocean current is traveling due south at a speed of 5 km/hour. How long will it take the ship to travel a distance of 10 km? The bottle in the animation drifts with the current.