An aircraft is flying wings level at constant altitude, at a speed of 500 ft/s, with an angle of attack of 8∘ and a sideslip angle of −5∘, when it runs into gusty wind conditions. Determine the new "instantaneous" angles of attack and sideslip angle for the following cases:

(i) A horizontal gust of 20 ft/s from left to right along the body y-axis

(ii) A horizontal gust of 50 ft/s from dead astern

(iii) A gust of 30 ft/s, from the right, with velocity vector in the y-z plane, and at an angle of 70∘ below the x-y plane