Team Number
Grade 8
Problem Solving
Lin
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Team Number:
2. (a) The ceiling of the cave has equation x+3y-33. Find the points the ceiling intersects the
boundary of the screen. Give your answer as a mixed
number if necessary and explain your
answer using algebra.
(b) The player character stands at (0,0), so the floor of the cave contains the point (0,0). The
cave floor has a slope of 1
Find the points the floor intersects the boundary of the screen.
Give your
answer as a mixed number if necessary and explain your answer using algebra.
10
For his demo, Tim will assume the flashlight points in a straight line, with varying slope, but always
containing the point (0,3) (where the player character would hold the
flashlight). For the questions
below, ignore that a real flashlight's
beam has width, and assume it just travels on the line.
3. For each of the slopes given in (a) and (b) below, answer the following
(i) Where does the flashlight intersect the cave ceiling? Which direction is the player character
facing? Is this
intersection actually on the screen? Show your work and explain your answer.
(ii) Where does the flashlight intersect the cave floor? Which direction is the player character
facing? Is this
intersection actually on the screen? Show your work and explain your answer.
Note: If the flashlight does not intersect the cave ceiling or floor, say so.
(a) Flashlight slope of -2
(b) Flashlight slope of
1
10
4. The final addition to Tim's demo will be a bat that flies horizontally starting at the point (-10, 9).
The bat flies at a speed of 2 units per second.
(a) What is the bat's position after 3 seconds? What is the slope of the flashlight if it is pointed
directly at the bat? Show your work, including a diagram showing the solution on the answer
sheet. Include the bat and the path of the flashlight in your diagram.
(b) What is the bat's position after 8 seconds? What is the slope of the flashlight if it is pointed
directly at the bat? Show your work, including a diagram showing the solution on the answer
sheet. Include the bat and the path of the flashlight in your diagram.
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