Dorothy's Flying!

Calculus Level 3

x ( t ) = t cos ⁡ ( 2 t ) y ( t ) = t sin ⁡ ( 2 t ) x(t) = t\cos(2t) \\ y(t) = t\sin(2t)

Dorothy's house in Kansas was blown upwards into the tornado, and Dorothy's position can be formulated as shown above.

What is the distance between the 2 adjacent spiral branches on the x-y plane?

π 4 \dfrac{\pi}{4} 4 π 4\pi π \pi 2 π 2\pi π 2 \dfrac{\pi}{2}

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Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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1 solution

The spirals in this problem is the simple form of the Archimedes' spirals. If we draw a line from the point of origin to intersect the outward spirals, the distance between two consecutive spirals will be the same. For example, in the image above, from the point of origin towards the positive x-axis, the spirals intersect with equal periods of π \pi .

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