Raindrop: the force on a small raindrop is f = m dv/dt = - yv- mg (in the y-direction.) a. find a substitution u(t) in terms of v(t) that gets rid of the pesky gravity term in the equation above, leaving you a formula similar (not necessarily identical) to .= y* u(t). b. take the indefinite integral of both sides of the formula. be careful with the constant(s) c; what happens to it/them when you take the exponential of both sides? c. substitute (t) back in, so you have a formula for the velocity of the raindrop as a function of time. d. assume the raindrop started from rest, v(t = 0) = 0. solve your equation for the unknown constant, so you have v(t) for all times t 0. e. what is the maximum velocity of the raindrop, vmax? f. the quantity m/y has units of time. discuss (1-2 sentences) the meaning m/y. g. how long does it take for the raindrop to reach 63% of its maximum velocity? 87.5%? 95%? give this in terms of m/y, and explain in a grammatically correct sentence with words) why i chose those specific what links them?