Question

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I need the full worked solution (step-by-step with clear explanations where possible) for all parts of this question, please. The final answers to all the parts are given below the questions. Would greatly appreciate neat handwriting with clear steps. Thank you! :)

Question 6 A particle of mass m is projected vertically upwards with an initial speed vo in a fluid. The magnitude of the resistive force is kv, where v is the speed of the particle and k is a constant of proportionality. The origin is taken at the point of projection of the particle, and the unit vector i points in the upward direction. Define an appropriate coordinate axis, draw a force diagram showing all the forces acting on the particle during ts upward motion. Express each force in (a) vector terms. (4 marks) (d) Show that the greatest height Xmax, the particle reaches above the point of projection is given by 訓甼) (2 marks) For the downward motion, take the origin to be the point of greatest height, with the unit vector i pointing vertically downward. (e) Draw a force diagram showing all the forces acting on the particle during its (2 marks) (f Present the equation of motion for the particle during its downward motion and (3 marks) (g) Solve this differential equation during its downward motion, to obtain an 4 marks) downward motion. Express each fore e in vector terms. hence find the terminal speed vT of the particle in terms of expression for the displacement of the particle x from the origin, in terms of v, and g Answers: 6. (a) During its upward motion, Weight, w--mgi ; Resistive Force, R--hi (e During its downward motion, Weight, W-mgi vr_λ Resistive Force, R-kvi (f) (g) X=

Answer 1

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