(e) Solve your initial value problem for v(t). You can use separation of variables or go by an integrating factor. (f) Use your result in step 'e' to find the position function x(t). ONLY PART E AND F, please and thank you!
An object of mass 100 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy force of 1/40 times the weight of the object is pushing the object up (weight = mg). Assume that water resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10 N-sec/m. Answer the following questions. (a) Find the force due to gravity. Use g = 9.81 m/sec^2. (b) Find the buoyancy force. (c) Express the air resistance force using the given information. (d) Use Newton's second law to build a differential equation for the velocity v(t). What is the initial data? (e) Solve your initial value problem for v(t). You can use separation of variables or go by an integrating factor. (f) Use your result in step 'e' to find the position function x(t). ONLY PART E AND F, please and thank you!
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An object of mass 100 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy force of 1/40 times the weight of the object is pushing the object up (weight = mg). Assume that water resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10 N-sec/m. Answer the following questions. (a) Find the force due to gravity. Use g = 9.81 m/sec^2. (b) Find the buoyancy force. (c) Express the air resistance force using the given information. (d) Use Newton's second law to build a differential equation for the velocity v(t). What is the initial data? (e) Solve your initial value problem for v(t). You can use separation of variables or go by an integrating factor. (f) Use your result in step 'e' to find the position function x(t). Part D ONLY! Please and thank you.
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