Question: Suppose that a spherical raindrop falling through a moist atmosphere grows at a rate proportional to its surface area. (a) Explain why dV/dt = kV2/3

Suppose that a spherical raindrop falling through a moist atmosphere grows at a rate proportional to its surface area.
(a) Explain why dV/dt = kV2/3 k a positive constant, models this situation.
(b) Demonstrate non-uniqueness for dV/dt = k V2/3, V(0) = 0, by constructing several solutions.

Step by Step Solution

★★★★★

3.30 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a We are given dVdt kA where A is the surface area of the raindro... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

947-M-L-A-L-S (4550).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

When a bottle of liquid refreshment was opened recently, the following factoid was found inside the bottle cap: The average velocity of a falling raindrop is 7 miles/hour. A quick search of the...

Suppose that a spherical droplet of liquid evaporates at a race that is proportional to its surface area. dV/dt = kA Where V = volume (mm 3 ), t = time (h), k = the evaporation rater (mm/hr), and A...

Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer...

A spherical raindrop 2.1 mm in diameter falls through a vertical distance of 3650 m. Take the cross-sectional area of a raindrop = r, drag coefficient = 0.45, density of water to be 1000 kg/m, and...

To maintain a constant speed, the force provided by a car's engine must equal the drag force plus the force of friction of the road (the rolling resistance). The density of air is 1.2 kg/m3. (a) What...

MY NOTES A block of mass m, = 34 kg on a horizontal surface is connected to a mass m, = 22.6 kg that hangs vertically as shown in the figure below. The two blocks are connected by a string of...

Py 211 module 16 Problem 1 You are helping your friend move a new refrigerator into his kitchen. You apply a horizontal force of 265 N in the negative Wm try and move the 59 kg refrigerator. The...

PY 211 North Carolina State University Module 16 Problem 7 To maintain a constant speed, the force provided by a car's engine must equal the drag force plus the force of friction of the road (the...

A spherical raindrop 1.7 mm in diameter falls through a vertical distance of 4400 m. Take the cross-sectional area of a raindrop = Irrz, drag coefcient = 0.45, density of water to be 1000 kg/m3, and...

A spherical raindrop 3.1 mm in diameter falls through a vertical distance of 4300 m. Take the cross-sectional area of a raindrop = a, drag coefficient = 0.45, density of water to be 1000 kg/m, and...

What can multinational corporations do to encourage corporate social responsibility among the companies with which they do business abroad?

In the unbalanced transportation problem in the table, if a unit from a source is not shipped out (to any of the destinations), a storage cost is incurred at the rate of S4, $5, and $3 per unit for...

When a bond is issued with contract rate > market rate, what is this called?

(Market for Pollution Rights) The graph in page 302 shows the market for pollution rights. a. If there are no restrictions on pollution, what amount is discharged? b. What is the quantity supplied...

In Problems 32 through 36, writein the manner of Eqs. (3) through (6) of this sectiona differential equation that is a mathematical model of the situation described. The acceleration dv=dt of a...

In Problems 31 through 42, verify that the given differential equation is exact; then solve it. (3x + 2y2) dx + (4xy + 6y2) dy = 0

Problems 33 and 34 explore vertical motion on a planet with gravitational acceleration different than the Earths. A person can throw a ball straight upward from the surface of the earth to a maximum...

QUESTION 1 [25 MARKS] The following statement of financial position information relates to Tura Co, a company listed on a large stock market which pays corporation tax at a rate of 30%. N$m N$m...

Project A has cash flows of $50,000,$49,400,527,200, and $24,500 for Years 0 to 3 , respectively. Project B has an initial cost of $50,000 and an annual cash inflow of $18,500 for four years. These...

Pricing Stock Issues in an IPO Zang Industries has hired the investment banking firm of Eric, Schwartz, & Mann (ESM) to help it go public. Zang and ESM agree that Zang's current value of equity is...