this is the whole task with all the information given The map below shows the flight path for someone traveling from Washington DC and passing above Indianapolis, Indiana; Lincoln, Nebraska $($hometown of the University of Nebraska High School!$)$ and landing in San Francisco. 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$).$

$1.$ 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?