Investigation

Relating Height and Time at Canada’s Wonderland

At Canada’s Wonderland, visitors can choose from a wide variety of rides.

Rage is a large ship that swings higher and higher. At its highest position, people on the ride feel as if they will fall out of their seats.

Imagine that you are on Rage.

  1. Visualize how high above the ground you are as the ride progresses from the beginning to the end.
  2. Which graph below best represents the relationship between your height above the ground and the elapsed time? Explain your choice.

Drop Tower is a 23-storey free-fall ride. People in open cockpit seats are lifted to the top of the ride, where there is a brief stop. Then they are dropped straight down, reaching speeds of 100 km/h before coming to a complete stop.

Imagine you are on Drop Tower.

  1. Visualize how high above the ground you are as the ride progresses from the beginning to the end.
  2. Which graph below best represents the relationship between your height above the ground and the elapsed time? Explain your choice.

Exercises:

  1. Which graph below best represents each scenario?
  2. The height of a tree over time.
  3. The height of a Ferris Wheel seat as the wheel rotates.
  4. The number of hours you might sleep each day over your whole lifetime.
  5. The number of computers sold, compared to the selling price.
  1. This graph shows the height of the water in a bathtub over a period of time. Describe what happened to the water in the bathtub. Think about the name on each axis and the points where the graph intersects the axes, as well as possible reasons for the changes at the points indicated

  1. People who give speeches sometimes get instant feedback from the audience. Audience members use an electronic device to indicate whether they agree or disagree with what the speaker is saying at the moment. The results are averaged and displayed in graphical form on a monitor visible to the speaker. Two complete graphs are shown.
  2. Describe the audience reaction to each speech.
  3. Which speech do you think the audience found more interesting? Explain.
  1. This graph shows the speed of Raoul’s bike as he rides from home to school. Write a possible description of Raoul’s journey.
  1. Draw a graph, with clearly labelled axes, to fit each activity. Decide which quantity to plot along the vertical axis and which quantity to plot along the horizontal axis.
  2. A person running a 3000m race around a track.
  3. A person walking along a level road, climbing a hill, stopping to rest at the top, then walking back down the hill.
  4. A person diving off a diving board.
  5. A ski jumper jumping during a competition.
  6. An alpine skier skiing in a slalom race.
  1. In a science experiment, student suspended an object on a spring, then pulled the object down and released it to measure its motion. The graph displays the height of the object above the floor during the first few seconds of the experiment.
  2. Find the height of the object after 1s, 2s and 3s.
  3. Find when the object was 6cm above to floor; 10cm above the floor.
  4. Find how long it takes the object to move up and down once.
  5. How does the height change during each of the first 3 seconds.
  6. For each answer in part d, describe how the object is moving relative to the floor.
  7. Suppose the students continued to measure the motion of the object for 5 minutes, then plotted the graph. Describe how you think the graph would look. Explain your thinking.