(Originais Teachy 2023) - Question Medium 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.

João is helping his father fill the home pool, which is rectangular and has the following dimensions: 8 meters in length, 4 meters in width, and 1.5 meters in depth. They are using a hose with a constant flow rate of 20 liters per minute. Considering that the pool was completely empty and there was no water wastage in the process, answer: (a) What is the total volume of the pool in liters? (b) How long, in hours, will it take to completely fill the pool with the hose? (c) If the water in the pool had the mentioned constant flow rate, but drained through an opening of the same size as the hose, how long would it take for the pool to completely empty?

A motor operates according to the Carnot cycle between two thermal sources. The hot source is at a temperature of 500 K and the cold source at 300 K. Determine the efficiency of the motor, knowing that the efficiency of the Carnot cycle is calculated by the expression 1 - (Tcold/Thot), where Tcold and Thot are the temperatures of the cold and hot sources, respectively. Discuss briefly the importance of the maximum efficiency of the Carnot cycle in practical applications of thermal engines.