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📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A student builds a drone that ascends vertically at 4 m/s while expanding a rectangular grid of sensors covering a volume of 1,440 m³ per minute. If the grid width increases at 2 m/s and height at 3 m/s, what is the current width of the grid?

📌 Volume flow rate: dV/dt = area × velocity in depth × rate of expansion? But assume sensor grid expands uniformly in width and height at constant rates.

📌 Let width = w, height = h, length = l. Given: dl/dt = 4 m/s, dh/dt = 3 m/s, width increases at 2 m/s ⇒ dw/dt = 2

📌 Volume = w × h × l = 1,440 m³ (current state)

📌 But we need rate: dV/dt = (dw/dt)(h)(l) + w(dh/dt)(l) + w×h(dl/dt)

📌 But dl not a depth variable; reinterpret: the grid expands in width and height at constant velocities, and length is constant? But not specified.

📌 Assume volume at any time: V = w(t) × h(t) × l (fixed length). But length unknown.

📌 Alternate: assume the rate of volume increase arises from expansion. But simpler: assume length is constant and expands with width and height? Not realistic.

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