A 50-lb box shaped like a 1-ft cube falls from the cargo hold of an airplane at an altitude of \(30,000 \mathrm{ft}\). If the drag coefficient of the falling box is 1.2, determine the time it takes for the box to hit the ocean. Assume that it falls at the terminal velocity corresponding to its current altitude and use a standard atmosphere (see Table C.1).

Table C.1

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Properties of the U.S. Standard Atmosphere (BG/EE Units)* Acceleration Density, Altitude (ft) Temperature (F) of Gravity, g (ft/s) Pressure, p [lb/in.(abs)] (slugs/ft)b Dynamic Viscosity, (lbs/ft) -5,000 76.84 32.189 17.554 2.745 E 3 - 0 59.00 32.174 14.696 2.377 E-3 5,000 41.17 32.159 12.228 2.048 E-3 3.836 E 7 3.737 E 7 3.637 E 7 - - 10,000 23.36 32.143 10.108 1.756 E-3 3.534 E-7 15,000 5.55 32.128 8.297 1.496 E 3 3.430 E 7 20,000 -12.26 32.112 6.759 1.267 E 3 3.324 E-7 25,000 -30.05 32.097 5.461 1.066 E 3 - 3.217 E 7 30,000 -47.83 32.082 4.373 8.907 E-4 3.107 E 7 - 35,000 -65.61 32.066 3.468 7.382 E 4 2.995 E 7 - 40,000 -69.70 32.051 2.730 5.873 E 4 2.969 E 7 - 45,000 -69.70 32.036 2.149 4.623 E 4 2.969 E 7 50,000 -69.70 32.020 1.692 3.639 E 4 - 2.969 E-7 60,000 -69.70 31.990 1.049 2.256 E - 4 2.969 E-7 70,000 -67.42 31.959 0.651 1.392 E 4 - 2.984 E 7 - 80,000 -61.98 31.929 0.406 8.571 E 5 3.018 E 7 90,000 -56.54 31.897 0.255 5.610 E-5 3.052 E-7 100,000 -51.10 31.868 0.162 3.318 E 5 3.087 E 7 150,000 19.40 31.717 0.020 3.658 E -6 3.511 E-7 200,000 -19.78 31.566 0.003 5.328 E-7 3.279 E 7 - 250,000 -88.77 31.415 0.000 6.458 E - 8 2.846 E 7 -