Question

A frog jumps to the left with an average speed of 1.8\,\dfrac{\text m}{\text s}1.8 s m ​ 1, point, 8, start fraction, start text, m, end text, divided by, start text, s, end text, end fractionfor 0.55\,\text s0.55s0, point, 55, start text, s, end text. What was the frog's displacement in meters?

Answer 1

Answer:

A frog starts at (0,0) on the Cartesian plane, and each minute jumps a

distance of exactly 1 unit to a point with rational coordinates.

(a) Show that it is possible for the frog to reach the point (1/5,1/17)

(b) Show that the frog can never reach the point (0,1/4)

I'm not sure, but I think this is one way you can do it. For part (a),

draw the circle with radius 1 and center (0,0) and also with radius 1

and center (1/5,1/17). Where these two circles intersect is where the

frog can jump to from (0,0) and then it will also be 1 unit away from

(1/5, 1/17) since it is the intersection of the two points. We just

need to show that the intersection of the two circles occurs on a

point with rational coordinates.

Similarly, you can do that with the point (0,1/4), and show that the

intersections of the two circles does not occur on rational coordinates.

I only have two issues with this way:

1) I don't know how to find the intersection points of two circles

2) The method I used only has the frog moving twice. There might be a

way the frog can go to the given coordinates in more than 2 moves.

Help is very much appreciated :)

Answer 2

Answer:

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Explanation:

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