Could you please help with the following question? part(b) and (c) please give the detailed solving process. How do you integrate? and how to take limit and prove it's E.S

1. For this entire problem, assume an object of mass m falls from rest, starting at a point near the Earth's surface. We discussed the free-fall model with air resistance proportional to the velocity of the object (see section 1.4 of our text). For this problem we will investigate a free-fall model with air resistance proportional to the square of the velocity F, = :tlc'v2, where ls > 0 is a constant of proportionality depending on the size and shape of the object, as well as the density and viscosity of the air. The square model has been shown to be more appropriate for some objects at high speeds. (a) Taking the positive direction downward (as in the linear air resistance model in section 1.4) and assuming F, is proportional to 1:2 as mentioned above, model a differential equation for the velocity of the object v(t), similar to equation 1.4.10 on page 38. Warning: make sure your resistance term has the correct sign. (b) Find the general solution to the equation in part (a) and apply your initial condition to nd the particular solution below, explicitly solving for v(t): v(t) = @tallh (Er) , where tanh(m) = Bap8% is hyperbolic tangent. Hint: The integral formula should be helpful a! 1 fu u _ _ u a 2aln|u_a|+(3'. a2u2 (c) Take limHth) to nd the terminal velocity W. Show that v = UT is an equilibrium solution