(b) Suppose the raindrop accretes mass at rate dm/dt = bmv with b > 0. i) Show that the speed of the raindrop falling under the force of gravity at time t is v (t) = √ √ 7/1 tanh(V/gbt), with initial condition at t = 0, v(0) = 0. ii) Compute m(t) given the initial conditions that at t = Hint: The following integral may be of use So tanh(at')dt' = 0, m(0) = mį. ¹ In(cosh(at)). a
(b) Suppose the raindrop accretes mass at rate dm/dt = bmv with b > 0. i) Show that the speed of the raindrop falling under the force of gravity at time t is v (t) = √ √ 7/1 tanh(V/gbt), with initial condition at t = 0, v(0) = 0. ii) Compute m(t) given the initial conditions that at t = Hint: The following integral may be of use So tanh(at')dt' = 0, m(0) = mį. ¹ In(cosh(at)). a
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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