Homework Assignment 3
Due March 1, 2008

1. Solve the Bicycle Rider problem from the textbook in three different ways. Be sure to write your programs so it will be easy to change the variables (power P, mass M, frontal area A, air density rho, etc.) used.
   1. A C program using the Euler method to solve the differential equation.
   2. A C program using the fourth order Runge-Kutta method to solve the differential equation.
   3. A MATLAB program using the ode45 function to solve the differential equation.
2. Use the three methods to solve for a rider mass of 70 kg, a power of 400 watts, and an air resistance of 0 (i.e., no drag). For the C programs, use a dt of 1 second. Compare the speed at time 200 seconds to the analytical result. (With no drag, the analytical result is given be Equation 2.5 of the text.)
3. For this part, use the program which gave the closest match to the analytical result.
   1. How much more power does a rider who weighs 75 kg have to generate to achieve the same terminal speed as a rider who weighs 70 kg? (Use a power of 400 watts, an area of 0.33 m^2, and an air density of sea level).
   2. Equation 2.20 of the text shows an approximate expression for air denisity as a function of altitude. How much faster can a rider go at an elevation of 10,000 ft. compared to his/her speed at sea level? (Use a mass of 70 kg, a power of 400 watts, and an area of 0.33 m^2.)
   3. A bike manufacturer produces equipment which can reduce the drag by 1%. How much does a 1% change in the drag (reducing C from 0.50 to 0.495 in Equation 2.10) increase the terminal speed? (Use a mass of 70 kg, a power of 400 watts, an area of 0.33 m^2, and an air density of sea level).