Plane's speed: 180 miles per hour The figure shows a small plane flying at a speed of 180 miles per hour on a bearing of N49 E. The wind is blowing from west to east at 47 miles per hour. The figure indicates that v represents the velocity of the 490 plane in still air and w represents the velocity of the wind. Wind's speed: 47 miles per hour v = 180 cos 41 i + 180 sin 41 j; w = 47 cos 0i + 47 sin 0j CV = 180 sin 41 i + 180 cos 41 j; w =47 sin 0i + 47 cos 0"j D. V = 180 cos 49 i + 180 sin 49 j; w =47 cos 41"i + 47 sin 41"jPlane's speed: 180 miles per hour The figure shows a small plane flying at a speed of 180 miles per hour on a bearing of N49 E. The wind is blowing from west to east at 47 miles per hour. The figure indicates that v represents the velocity of the 190 plane in still air and w represents the velocity of the wind. Wind's speed: 47 miles per hour b. Find the resultant vector, v + W. V + W= (Simplify your answer. Type an integer or decimal rounded to the nearest hundredth as needed. Type your answer in the form ai + bj.)b. Find the resultant vector, v + W. To find v + w, first simplify v = 187 cos 38i + 187 sin 38 j and w =51 cos 0i + 51 sin 0 j. Then add v and w. Simplify v = 187 cos 38 i + 187 sin 38'j. V = 187 cos 38 i+ 187 sin 38 j ~147.36i + 115.13j Use a calculator set to degree mode. Next simplify w = 51 cos 0i + 51 sin 0 j. w = 51 cos 0 i + 51 sin 0 j ~ 51i Use a calculator set to degree mode. Now find v + w.Now find v + w. V + w = 147.36i + 115.13j + 51i Use v and w found above. ~ 198.361 + 115.13j Add the horizontal components, add the vertical components, and simplify