He velocity vector field for a fluid flowing in 3 is given by v = xz, −yz, y m/s. let s be the oriented surface that is the portion of the plane x + y + z = 3 in the first octant with upward orientation n. compute the amount of fluid crossing s per second in the direction of n.

The ratio of lift to drag l/d for a wing or airfoil is an important aerodynamic parameter, indeed, it is a direct measure of the aerodynamic efficiency of the wing. if a wing is pitched through a range of angle of attack, l/d first increases, then goes through a maximum, and then decreases. consider an infinite wing with an naca 2412 airfoil. estimate the maximum value of l/d. assume that the reynolds number is 9x10^6.

An alien spaceship is 500 m above the ground and moving at a constant velocity of 150 m/s upwards. how high above the ground is the ship after 5 seconds?

Wo small variable-thrust jets are actuated to keep the spacecraft angular velocity about the z-axis constant at ? 0 = 1.16 rad/s as the two telescoping booms are extended from r1 = 1.18 m to r2 = 4.69 m at a constant rate over a period of 124 seconds. the small 19-kg experiment modules at the ends of the booms may be treated as particles, and the mass of the rigid booms is negligible. determine the necessary thrust t for each jet as a function of time where t = 0 is the time when the telescoping action is begun. after you have the general expression for t, answer the questions. show work.