When a raindrop falls, it increases in size and so its massat time t  is a function of t , m(t) . The rate of growth of themass is km(t) for some positive constant . When weapply New ton’s Law of Motion to the raindrop, we get (mv)' = gm, where is the velocity of the raindrop(directed downward) and g is the acceleration due to gravity.The terminal velocity of the raindrop is lint→∞ v(t) . Find anexpression for the terminal velocity in terms of  g and k .

Q: (b) Suppose the raindrop accretes mass at rate dm/dt = bmv with b > 0. i) Show that the speed of the…

A: Given the equation of motion of mass accretion is mdvdt+vdmdt=F. (b) It is given that the rain drop…

Q: Suppose an object is moving along a line such that the acceleration after t seconds is 6t -8t…

A:

Q: Use implicit differentiation to find dv/dL.

A: We will use concepts of differentiation in this.

Q: dt' Population growth is commonly modeled upon the simple statement that the popu- lation growth…

A:

Q: A(t) = 3000e027z initial investment of 3000 dollars which pays 2.7% compounded continuously. a) Find…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.