Suppose that a parachutist with linear drag (m=50 kg, c=12.5kg/s) jumps from an airplane flying at an altitude of a kilometer with a horizontal velocity of 220 m/s relative to the ground. a) Write a system of four differential equations for x,y,vx=dx/dt and vy=dy/dt. b) If theinitial horizontal position is defined as x=0, use Euler’s methods with t=0.4 s to compute the jumper’s position over the first 40 s. c) Develop plots of y versus t and y versus x. Use the plot to graphically estimate when and where the jumper would hit the ground if the chute failed to open.

1. Assume that a function f is in polynomial time and can be computed in time 0(n) and that g is in polynomial time and can be computed in time 0(n°). Prove that f composed with g, that is f(g(x)), can be computed in time 0(n5).

- 4. Let = (1, 2, 1), 7 (-1,-1, 2) and w= (0,3,2). Show that ü, 7 and w are linearly dependent or independent. 5. Let = (0, 2, 1), 7 (-1,0, 2) and = (2,3,0). Find the coordinates of (2,2,2) with respect to the basis u, u and w.