compute the numerical values of (u, v) for the following case: = 27 m/s, 1 = 2,0 3 x = 1, y = 1, x = 3, y = 4 J More formulas: Appendix: Useful Mathematical Formulas cos0 1 d + (b-t) t d + (b-t) t(b-t) d + (b 1) where b and d are constants. dt Va dt -1 -(tan x): = -ln(x): d dx d dx d dx X sin x + cosx = 1 dt -(tan()) X 7- 2 a + x -dx = = 1 + cos(20) 2 1 a 1 - 1+x b -1 tan tan -td tan -y x + y tan X - dx = = - In(a a + x X 1 a 1 ( 7 ) + 1/ m [d + (b 1)] In d -In(a+x) b 1 ( b = ) - 1/2 [d + (6 1)] In tan^' (ax) dx =x tan^ (ax) __ln(1 + ax) 2a -1 X [ ln(x + a)dx =x ln(x + a) 2x+2a tan a a -1 [Tax + (2) dx = x tan " (# )+ - (1 + 5 ) -1 Stan =x a +ln X X a (1) (2) (3) (4) Problem 2: Consider a general uniform source panel of the total length / lying at an angle = [0, 2] as shown in Fig. 3. The center O' of the panel is at (x, Yo): E y y O Hol +XXI = const '( v I' P(x,y) x Fig. 3. A straight source panel of uniform strength along the horizontal direction.