(Originais Teachy 2023) - Question Very Easy of Physics

An airplane initially flies north at a speed of 200 km/h. Due to a wind blowing from east to west, the airplane ends up deviating to the northeast, following a trajectory that forms a 45-degree angle with the north direction and covering a distance of 300 km from the starting point. Determine, using vector concepts, the speed of the airplane relative to the ground, considering the effect of the wind. Consider that the wind speed is constant and equal to 50 km/h, and that the wind direction is perpendicular to the initial direction of the airplane.

A student is observing an object through a converging lens with a focal length of 10 cm. The object is located 40 cm away from the lens. (Consider that the thin lens approximation is valid). Based on this information: 1) Calculate the position of the image formed by the lens. 2) Determine the size of the image relative to the size of the object, knowing that the lens obeys the Gauss equation (1/f = 1/p + 1/p'), where f is the focal distance of the lens, p is the distance from the object to the lens, and p' is the distance from the image to the lens, all measured in cm. Consider that the coordinate system used has its origin at the lens's optical center, with the main axis oriented positively to the right, and that real images have a positive sign and virtual images have a negative sign.