How to Navigate an Airplane with Wind: A Fun Physics Problem!

What direction should the pilot head her plane if there is a 75 km/h wind blowing toward the east?

a) Due North b) Due East c) North-East d) North-West

Answer:

The pilot should head the plane slightly eastward of due north to compensate for the eastward blowing wind.

Have you ever wondered how airplane pilots navigate through different wind conditions? Let's explore an interesting physics problem involving an airplane pilot flying due north with a 75 km/h wind blowing toward the east.

To determine the direction the pilot should head her plane, we need to consider vector addition. In this case, we have two vectors: the velocity vector of the airplane in calm air (310 km/h due north) and the velocity vector of the wind (75 km/h due east).

If we represent these vectors graphically, we create a right triangle where the airplane's velocity is the hypotenuse and the wind's velocity is one of the legs. The resultant velocity of the airplane, the sum of the airplane's velocity and the wind's velocity vectors, determines the direction the pilot should head her airplane.

By using the Pythagorean theorem, we can calculate the resultant velocity. However, to find the direction, we employ trigonometric functions. Specifically, we use the tangent function, which equals the wind's velocity divided by the airplane's velocity. This gives us the angle at which the pilot needs to point her plane slightly eastward of due north to counteract the eastward wind.

Physics problems like this one are not only educational but also fascinating to solve. They demonstrate how principles of physics apply in real-world scenarios, such as piloting an aircraft. Next time you look up at the sky and see an airplane soaring through the clouds, remember the intricate calculations and adjustments the pilot must make to ensure a safe and efficient flight!