Given a physical situation (e.g., a room of a certain shape and dimensions, with objects at certain positions and a robot moving across the room), students impose a coordinate system and describe the given in terms of polygonal regions, line segments, and points in the coordinate system.
Searching a Region in the Plane
Students in a robotics class must program a robot to move about an empty rectangular warehouse. The program specifies location at a given time 𝑡 seconds. The room is twice as long as it is wide. Locations are represented as points in a coordinate plane with the southwest corner of the room deemed the origin, (0,0), and the northeast corner deemed the point (2000,1000) in feet, as shown in the diagram below.
The first program written has the robot moving at a constant speed in a straight line. At time 𝑡 = 1 second, the robot is
at position (30,45), and at 𝑡 = 3 seconds, it is at position (50,75). Complete the exercises, and answer the questions
below to program the robot’s motion.
a. At what location will the robot hit the wall?
b. At what speed will the robot hit the wall?
c. At what time will the robot hit the wall?
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