A room has dimensions 3.05 m(height) x 3.85 (width) m x 4.15 (length) m. A fly s

Question

A room has dimensions 3.05 m(height) x 3.85 (width) m x 4.15 (length) m. A fly starting at one corner flies around, ending up at the diagnolly opposite corner.

a.) what is the magnitude of its displacement?

b) could the length of its path be less than this magnitude, yes or no?

c) could the length of its path be greater than this magnitude, yes or no?

d) could the length of its path be equal to this magnitude, yes or no?

e) take x,y, z axes so that the x-axis is parallel to the width, the y axis is paralle to the length, and the z-axis is parallel to the height. Express the components of the displacement vector. (__, ___, ___) meters

f) if the fly walks rather than flies, what is the length in meters of the shortest path it can take? Hint: this can be answered without calculus. The room is like a box. Unfold the walls and flatten them into a plane.

Explanation / Answer

a. magnitude of Dislacement = R^2 = (3.05^2 + 4.15^2 + 3.85^2)

so

R = 6.43 m

----------------------------------

b. NO

c. Yes

d. Yes

e. (W, L ,B ) = (3.85, 4.15, 3.05)

f. R^2 = W^2 + h^2

R^2 = 3.85^2 + 3.05^2

R = 4.911m

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