Vector Investigation -- Boat to Island

  • Vector Investigation – Boat to Island

    Grade: 6th to 8th, High School

    Move the boat around the water by changing the magnitude and direction of the boat's speed (blue vector) or the magnitude and direction of the water current (red vector). Try to land the boat on the island — but be careful not to hit the walls!

    Activity

    Instructions

    Modes

    • Static: Steer the boat to a stationary island.
    • Dynamic: Direct the boat to intercept a moving school of fish.
    • Game: Combines both static and dynamic challenges in a game setting. Earn points for reaching the destination.

    Settings

    • The magnitude and direction of the boat's speed (blue vector) is always active. It can be adjusted by dragging either end of the vector or by entering different numbers in the boxes along the right panel.
    • The magnitude and direction of the current of the water (red vector) can be toggled on and off. When on, it can be adjusted by dragging either end of the vector or by entering different numbers in the boxes along the right panel.
    • The result arrow (green vector) can be toggled on and off. It cannot be adjusted directly; it only represents the sum of the other two vectors.
    • The Start button allows the boat to depart from its current location.
    • The Reset button returns the boat to its original position.
    • The New Game button changes the initial location of the island (Static mode) or the fish (Dynamic mode).

    Exploration

    In Static mode, try to do three things:

    • Direct the boat to the island in just one shot with the red vector (water) turned off.
    • Direct the boat to the island in just one shot with the red vector (water) turned on. To do this, it may be helpful to turn on the result vector. How does the result vector relate to the boat and water vectors?
    • Set the magnitude and direction for both the boat and water vectors so the boat remains stationary. To accomplish this, what is the relationship between the boat and water vectors?

    Objectives and Standards

    NCTM Standards and Expectations
    • Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
    • 6-8
    • High School (9-12)
    • Geometry