It is proposed to dispose of nuclear wastes—in drums with weight W = 640 lb and volume 8 ft³—by dropping them into the ocean (v₀ = 0). The force equation for a drum falling through water is

where the buoyant force B is equal to the weight (at 62.5 lb/ft³) of the volume of water displaced by the drum (Archimedes’ principle) and F_R is the force of water resistance, found empirically to be 1 lb for each foot per second of the velocity of a drum. If the drums are likely to burst upon an impact of more than 75 ft/s, what is the maximum depth to which they can be dropped in the ocean without likelihood of bursting?

Transcribed Image Text:

m dv dt || -W+B+ FR.