When the effect of the air resistance is taken into account, the equation of motion for a particle of mass m falling vertically in a gravitational field is given by dt where g is the gravitational acceleration, and v- dy/dt is the velocity. The coefficient b specifies the strength of the interaction between the air and the particle. The initial conditions are y(0) 1000 m andv() 0 m/s Take n-1 kg and g = 9.8 ms-2 in the following (a) (30 marks) Write a C program that uses the Euler method to solve the above ODE. Consider the case without air resistance b 0. Plot y(t) against until y 0 (i.e., the particle has reached the ground) for two different time steps 1-ls and 0.01 s in one figure. Plot also the exact solution in the same figure for comparison. Submit your program and figure to th e TAs. (b) (20 marks) Fix the time step A 0.01 s in this part. Plot y(t) against until y 0 for four cases b 0,0.2,0.4,0.6 kg/s in one figure for comparison. Similarly, plot v(t) against for these four cases in one figure. [Note: Submit your figures to the TAs.]