Question

An ‘anti-drowning’ bracelet is a water safety device. It contains a CO₂ cartridge that can quickly inflate an airbag to help a diver rise to the surface in an emergency situation. Robert Irwin (son of “The Crocodile Hunter” Steve Irwin) is snorkeling at the Great Barrier Reef (ρ_seawater = 1029 kg/m³). He swims 5.0 m below the surface of the water when there is an emergency and he activates the bracelet. The mass of Robert and his gear is 69.2 kg and the volume of salt water he displaces is 0.07 m³ before the safety device is activated. Once he activates the device, it inflates to a volume of 0.01 m³. How long would it take him to get to the surface assuming he starts from rest (ignore any drag forces from the water)?

Answer 1

Using the Newton second law of motion: EF = ma B - mg = ma Then, the acceleration is: B a = -9 The buoyant force is. B = PwgVtotal = 1029(9.8) (0.07 + 0.01) = 806.736 N Then: 806.736 a = 69.2_-9.8 = 1.865 The time is. 2h / 5 t= va v 1.86 t = 2.32 s