Here we consider the situation where an object falls. We consider gravity and ai
ID: 2976611 • Letter: H
Question
Here we consider the situation where an object falls. We consider gravity and air resistance, assuming air resistance is proportional to the velocity and opposes the direction of motion. Suppose an object has mass 10 kg and is dropped from a high point and allowed to fall. Assume the value for g = 9.8 m/? s^2 . Assume the constant of proportionality for resistance is 3 (k = 3) The DE which describes this situation is 10 v'(t) = 98 - 3v(t), v(0) = 0 a) Is the DE separable? If so, write down the DE in the separable form. b) Is the DE linear? If so, what is the integrating factor? c) Is the DE autonomous? If so, what is the equilibrium solution, if any? Is the equilibrium solution stable? d) What is the numerical value of the terminal velocity? The solution to the IVP is v(t) = 98/3 - 98/3e^(-3t) e) Sketch the solution curve and the equilibrium solution. f) If the value for k were to increase, would the terminal velocity increase, decrease or stay the same (with all other values remaining the same)?Explanation / Answer
f) the terminal velocity increase