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When An insect flies from the corner a to the corner b of a cubic room in 5 seconds where a and b are diagonally opposite corners the side of the room is 5 metres.What is the speed of the insect?
Wiki User
∙ 14y ago
Approximately 1.73 m/s
Applying the Pythagorean theorem twice, you find that the diagonal of a cube with edge of length s is: s*sqrt(3).
[The diagonal of a face of a cube, dface, is found by: (dface)2=s2+s2=2s2 --> dface=s*sqrt(2).
dcube is find by applying the Pythagorean theorem to the triangle comprising sides of the diagonal of a face, an edge of the cube, and the diagonal of the cube:
(dcube)2=(dface)2+s2=2s2+s2=3s2 --> dcube=s*sqrt(3)
The speed of the insect is distance/time=5*sqrt(3)/5=sqrt(3) seconds, or approximately 1.73 m/s.
Wiki User
∙ 14y ago
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