Part B: Real World Problems (15 points each) Inmap below shows the fight path for someone traveling from vedsriington DC and passing aha, Indianapolis, Indiana ; Lincoln landing in San Fran incoln, Nebraska (hometown of the University of Nebraska High School!) and cisco. For the sake of clarity, we will assume that the plane is flying due west the entire trip The plane's engines put out enough power to fly at 545 mph if there is no wind ( but they could put out more if needed) New Hampshire Washington Vermont Massachusetts Maine Montana North Dakota Minnesota Oregon Wisconsin daho South Dakota New York Michigan Rhode Island Wyoming Pennsylvania Connecticut San Francisco Nevada NebraskaLincoln indianapolis Ohio New Jersey Indiana Delaware Colorado Maryland California Kansas Missouri Virginia Kentucky Washington, D.C. North Carolina Tennessee West Virginia Oklahoma Arizona Arkansas South New Mexico Carolina Mississippi Georgia Alabama Texa Louisiana 1. Please show all your work including both a diagram and algebraic solution. When the plane crosses over Indianapolis, the wind speed at flight altitude is 45 mph @ 45 degrees South of East. If the plane does not make any corrective action, the wind will both slow it down and knock it off course. Calculate the new velocity vector (both magnitude and direction) for the plane?2. Please show all your work including both a diagram and algebraic solution. When crossing over Lincoln, Nebraska, the plane runs into a headwind of 25 mph due East. If the plane does not make any corrective action, it will slow down and arrive in San Francisco late. How fast would the plane have to fly in order to maintain its intended speed and not lose any time? 3. Please show all your work including both a diagram and algebraic solution. When the plane crosses the border to Utah, it encounters a cross wind of 15 mph 5 degrees West of North. What speed and direction must the plane head in to keep going due West at 545 mph