Question

1. A robot from the video now moves around an empty 100 ft. by 100 ft. storage room at a constant speed. If the

robot crosses (10,10) at 1 second and (30,30) at 6 seconds:
a. Plot the points, and draw the segment connecting the points.
b. What was the change in the xx-coordinate?
c. What was the change in the yy-coordinate?
d. What is the ratio of the change in yy to the change in xx?
e. How far did the robot travel between the two points?
f. What was the speed of the robot?
g. Where did the robot start?

Answer 1

a). Graph attached

b). 20 ft

c). 20 ft

d). 1 : 1

e). 28.28 feet

f). 5.66 feet per second

g). (0, 0)

Explanation:

A robot crosses (10, 10) at 1 second and (30, 30) at 6 seconds with a constant speed.

a). As shown in the figure attached.

b). Change in x-coordinates = 30 - 10 = 20 feet

c). Change in the y-coordinates = 30 - 10 = 20 feet

d). Ratio of change in y to change in x coordinates =
`(20)/(20)`

= 1 : 1

e). Distance traveled by robot between these points =
`\sqrt{(x-x')^(2)+(y-y')^(2)}`

=
`\sqrt{(30-10)^(2)+(30-10)^(2)}`

=
`√(400+400)`

=
`20√(2)` feet

= 28.28 ft

f). Speed of the robot =
`\frac{\text{Distance covered}}{\text{Time taken to cover the distance}}`

=
`(20√(2))/((6-1))`

=
`(20√(2))/(5)`

=
`4√(2)`

= 5.66 feet per second

g). Robot stared from the origin (0, 0).