Water pours into the tank shown here at the rate of 4 ft³/min. The tank’s cross-sections are 4-ft-diameter semicircles. One end of the tank is movable, but moving it to increase the volume compresses a spring. The spring constant is k = 100 lb/ft. If the end of the tank moves 5 ft against the spring, the water will drain out of a safety hole in the bottom at the rate of 5 ft³/min. Will the movable end reach the hole before the tank overflows?

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Drain hole Movable end www ZZZ -5 ft- Side view Water in Movable end Drain hole Water in 4 ft 2 ft x x² + y² = 4