In this Gizmotm, a cat is 20 feet from a mouse hole and a mouse is between the cat and the hole. The cat sees the mouse and chases it. Will the cat catch the mouse? Follow the instructions below to find out.

  1. On the graph displayed in the Gizmo, the x-axis shows how long the cat and mouse have been running. The y-axis shows the distance of each animal from where the cat started. (Remember that the cat always starts 20 feet from the mouse hole.) Both graphs are linear because both animals run at a constant speed.
    1. On the CONTROLS panel, set the speed of the cat (Cat: average speed) to 1 foot per second. (To quickly set a slider to a specific number, type the number into the field to the right of the slider, and then press ENTER.) Using the slider, slowly increase the cat's speed. Does this affect the slope or the y-intercept of the cat's line in the graph? How does increasing the cat's speed affect the cat's chance of catching the mouse?
    2. Set the head start of the mouse (Mouse: head start) to 1 foot. Using the slider, slowly increase the head start of the mouse. How does this affect the mouse's line? How does increasing the mouse's head start increase the mouse's chance of reaching its hole safely?
  2. Use the Mouse: head start slider to give the mouse a 4-foot head start, use the Mouse: average speed slider to set the speed of the mouse to 4 feet per second, and use the Cat: average speed slider to set the speed of the cat to 5 feet per second.
    1. At the beginning of this simulation, how far is the mouse from the mouse hole? (Hint: The answer is not 4 feet.) How far is the cat from the mouse hole?
    2. Click SIMULATE. Does the cat catch the mouse?
    3. Click Show whether cat catches mouse. How far did the cat have to run to catch the mouse? For how many seconds did the animals run before the cat caught the mouse?
    4. Place your cursor over the point of intersection of the two lines on the graph. What are the coordinates of the point of intersection? What does the x-value of this point represent? What does the y-value represent?
    5. Use the Mouse: head start slider to give the mouse a head start of greater than 4 feet. Notice that the point of intersection of the lines on the graph is no longer visible. Will the cat catch the mouse now? Explain why or why not. Click SIMULATE to see if you were correct.
  3. Turn off Show whether cat catches mouse. Set the mouse's head start to 6 feet, the mouse's speed to 5 feet per second, and the cat's speed to 8 feet per second.
    1. What is the point of intersection of the two lines? How far did the cat run to catch the mouse? For how many seconds did the cat and mouse run? Click on Show whether cat catches mouse to check your answers. Then click on SIMULATE to see the chase.
    2. Click on the TABLE tab. The table displays the distances of the cat and mouse from the cat's starting point (Dmouse and Dcat) at every tenth of a second. There is only one row in this table in which Dmouse = Dcat. Find that row. (Use the scroll bar to the right of the table to see more values.) How do the values on this row relate to the point of intersection of the two lines?
  4. Graph two lines to represent each cat-and-mouse chase described below. Does the cat catch the mouse? If so, state how long the chase lasts, and how far the mouse is from its hole when it's caught.
    1. The mouse has a 4-foot head start. The cat and mouse both run at 8 feet per second.
    2. The mouse has a 7-foot head start, and runs at 9 feet per second. The cat runs at 16 feet per second.
    3. The mouse has a 6-foot head start, and runs at 10 feet per second. A super-fast cat runs at 40 feet per second.
    4. The mouse has an 3-foot head start, and runs at 4 feet per second. The cat runs at 5 feet per second.