Assignment:
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) = ?
Provide complete and step by step solution for the question and show calculations and use formulas.