Your younger brother who wishes to be a pilot reads a news article about a search and rescue plane. In this search and rescue operation, an ultra-light aircraft travelling north at 30 km/hr encounters a 40 km/hr crosswind. After explaining to him that a crosswind is wind that blows at right angle with the direction of the plane, he then asks you the following questions:

a. How fast and in what direction will the plane move as it gets affected by the crosswind?
b. Why is it important to understand the concepts of motion as a pilot?

a. X = 30km/h

Y = 40km/h

Tan A = Y/X = 40/30 = 1.33333
A = 53.13o E. of N. if wind is coming from the West. = 53.13o W. of N. if wind
is coming from the East.

V = Y/sin A=40/sin53.13=50 km/h[53.13o]

a. To determine how fast and in what direction the plane will move as it gets affected by the crosswind, you need to understand the concept of vector addition in physics. In this case, the plane's motion can be treated as the combination of its velocity relative to the ground (known as the groundspeed) and the velocity of the crosswind.

First, let's break down the problem. The plane is flying north at a speed of 30 km/hr, while the crosswind is blowing from the west at a speed of 40 km/hr. These velocities are given as magnitudes with respect to the ground. To find the resultant velocity, which represents the plane's motion relative to the ground, we can use vector addition.

To do this, we can draw a vector diagram. Let's draw a velocity vector pointing north with a magnitude of 30 km/hr (representing the plane's motion) and another vector pointing west with a magnitude of 40 km/hr (representing the crosswind). Since these vectors are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the resultant velocity vector. The direction of the resultant vector can be found using trigonometry, specifically the tangent function.

By applying these calculations, we find that the resultant velocity of the plane can be approximately 49.3 km/hr directed at an angle of 53.1 degrees northwest of due north. So, the plane will move at a speed of 49.3 km/hr and veer slightly towards the northwest relative to its intended northward course due to the crosswind.

b. Understanding the concepts of motion is crucial for pilots because it allows them to have better control over their aircraft and make informed decisions during flight. Here's why it's important:

1. Navigation: Pilots need to accurately determine their direction and how different factors, such as wind, affect their flight path. Understanding vector addition, as in the case of the crosswind, helps pilots calculate their groundspeed and choose the appropriate heading to reach their destination.

2. Efficiency: Knowing how different variables impact the aircraft's performance allows pilots to optimize their flight. By understanding concepts like airspeed, groundspeed, and fuel consumption, pilots can make adjustments to conserve energy and reduce costs.

3. Safety: Mastering motion concepts helps pilots anticipate and respond to changes in their flight environment effectively. It allows them to navigate through turbulent weather, avoid obstacles, and maintain stability during different flight conditions.

4. Decision-making: Understanding motion aids in decision-making during emergencies or unexpected situations. Pilots can assess their options and choose the best course of action based on their understanding of the aircraft's capabilities and the laws of physics that govern its motion.

Overall, a solid understanding of motion concepts empowers pilots to be more competent, confident, and skilled in their profession, ensuring safer and more efficient flights.