Purchase Solution

Velocity Differential Equation

Not what you're looking for?

Ask Custom Question

**Just need help with question 3, answers for 1 and 2 are provided***

A ping-pong ball is caught in a vertical plexiglass column in which the air flow alternates sinusoidally with a period of 60 seconds. The air flow starts with a maximum upward flow at the rate of 7m/s and at t=30 seconds the flow has a minimum (upward) flow of rate of -3.4m/s.

The ping-pong ball is subjected to the forces of gravity (-mg) where g=9.8m/s^2 and forces due to air resistance which are equal to k times the apparent velocity of the ball through the air.

1.) What is the average velocity of the air flow? 1.8m/s

2.) Write a formula for the velocity of the air flow as a function of time. 1.8+5.2cos(.1047197551t)

3.) Write the differential equation satisfied by the velocity of the ping-pong ball (relative to the fixed frame of the plexiglass tube.) The formulas should not have units entered, but use units to trouble shoot your answers. Your answer can include the parameters m - the mass of the ball and k the coefficient of air resistance, as well as time t and the velocity of the ball v. (Use just v, not v(t))

v'(t) = ?

Purchase this Solution

Solution Summary

This solution shows how to write a differential equation for a given problem.

Solution Preview

Net force (in upward direction) = mass*acceleration(in upward ...

Solution provided by:
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
Recent Feedback
  • " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
  • "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
  • "Answer was correct"
  • "Great thanks"
  • "Perfect solution..thank you"
Purchase this Solution

Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.