The famous illusionist harry houdini performed a trick where he escaped from being shackled in a packing crate that was lowered into the new york east river. an escape artist wants to perform a similar trick. the 70 kg escape artist with a density of 985 kg/m3, is to be locked in a cubic safe made from 1200 kg of steel. the waterproof safe has an outer volume of 1 m3 and 2.5 cm thick walls. the safe is to be dropped into a lake from the side of a boat whose deck is 2 m above water level. the escape artist expects to be able to escape the safe in 60s. a) derive the equations of motion for the safe, including buoyancy. clearly define the constants and assumptions in your equations. b) estimate how deep underwater will the illusionist escape the safe. you may make additional assumptions or use software to integrate the equations but they must be clearly explained.