3) [Friction] a) Write down the equation of motion for an object in a gravitational field...

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3) [Friction] a) Write down the equation of motion for an object in a gravitational field in the presence of linear friction. Choose the positive y-axis upward (opposite to gravity). Explain the sign in front of each of the terms that appear. b) Solve the differential equation subjected to the initial conditions y(t=0)=h and dy/dt(t=0)=0. c) Determine the terminal velocity of an object. d) Is the mechanical energy conserved? e) [576] Show that the result obtained in part b) agrees with the expected result in the case of vanishing friction. 3) [Friction] a) Write down the equation of motion for an object in a gravitational field in the presence of linear friction. Choose the positive y-axis upward (opposite to gravity). Explain the sign in front of each of the terms that appear. b) Solve the differential equation subjected to the initial conditions y(t=0)=h and dy/dt(t=0)=0. c) Determine the terminal velocity of an object. d) Is the mechanical energy conserved? e) [576] Show that the result obtained in part b) agrees with the expected result in the case of vanishing friction.