Assignment:
Q1. If air resistance is proportional to the square of the instantaneous velocity, then the velocity v of a mass m dropped from a given height is determined from:
m*dv/dt = mg - kv^2, k>0.
Let: v(0) = 0, k = 0.125, m = 5 slugs, and g = 32 ft/s^2
a) Use a fourth-order Runge-kutta (RK4) method with h = 1 to approximate the velocity v(5)
b) Use excel to graph the solution of the IVP on the interval [0,6].
c) Use separation of variables to solve the IVP and then find the actual value.
Q2. Find the analytic solution of the initial-value problem (IVP)
y' = -y +10sin(3x), y(0) = 0, on the interval [0,2].
a) Graph the solution and find its positive roots.
b) Use Runge-Kutta (RK4) method with h = 0,1 to approximate a solution of the initial-value problem (IVP)
Provide complete and step by step solution for the question and show calculations and use formulas.