91Ó°ÊÓ

To find the net displacement, we can break down the three flights into components and sum up the components to find the net displacement. 1. Flight 1: The pilot flies 55 mi west Horizontal displacement (west) = -55 mi (assuming east as positive and west as negative) 2. Flight 2: The pilot encounters ice and cannot land, so he flies 25 mi at \(15^{\circ}\) east of south. Horizontal displacement (east) = 25 mi * cos(\(15^{\circ}\)) = 25 mi * 0.9659 = 24.15 mi Vertical displacement (south) = 25 mi * sin(\(15^{\circ}\)) = 25 mi * 0.2588 = 6.47 mi (assuming north as positive and south as negative) Now, we will add up the displacements. Total horizontal displacement = -55 + 24.15 = -30.85 mi (west) Total vertical displacement = -6.47 mi (south) We will use the Pythagorean theorem to find the net displacement (distance). Distance = \(\sqrt{(-30.85)^2 + (-6.47)^2}\) = 31.7 mi (rounded to one decimal place) Finally, we will find the direction using the tangent function. Direction = arctan(\(\frac{-6.47}{-30.85}\)) = 11.9\(^{\circ}\) (rounded to one decimal place) So the pilot must fly 31.7 miles at 11.9\(^{\circ}\) west of south to reach his original destination.

To find the extra miles the pilot has flown, we will simply add the three distances he has traveled. Extra miles = 55 mi (west) + 25 mi (east of south) + 31.7 mi (west of south) = 111.7 miles Therefore, the pilot has flown 111.7 miles extra beyond his original flight plan.