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Imagine yourself moving in a car while observing the world around you. You might notice that static objects seem to "move" backward at the speed you're traveling, creating an illusion of motion. This phenomenon connects to the idea of relative velocity.
The term "relative velocity" describes how the velocity of one object appears from the perspective of another moving object. In our exercise, the snowflakes falling vertically appear to have a different motion when observed from the moving car.
Here's how it works: the car is moving horizontally at a speed of 13.89 m/s, while the snow is falling vertically at 8.0 m/s. The apparent movement of snowflakes combines these two motions. Consequently, this combination results in a diagonal path relative to the car's driver rather than the vertical descent perceived by a stationary observer.

Trigonometry is a branch of mathematics that explores the relationships in triangles, making it highly useful in physics problems involving angles. In our scenario, we leverage it to determine how the path of snowflakes changes with motion.
When we deal with vectors, particularly in two dimensions like our snow and car scenario, trigonometry becomes especially helpful. We can break down complex motion into simpler components. For the car and snowflakes, we observe two perpendicular components: horizontal and vertical. Then, we use these to form a right triangle.
The horizontal side of the triangle represents the car's speed, and the vertical side signifies the falling snow's speed. Trigonometry helps us understand how these components are related through functions like tangent, sine, and cosine, serving as tools to calculate angles and other key parameters.

Calculating angles using trigonometry involves knowing a bit about functions like sine, cosine, or tangent. In this exercise, to find out how the snowflakes appear to an observer in the moving car, we rely on the tangent function.
Here's a quick breakdown: The tangent of an angle in a right triangle is the ratio of the side opposite the angle to the adjacent side. For our exercise, the tangent function lets us relate the horizontal movement (car's speed) to the vertical movement (snow's speed).
By using the formula \[\tan \theta = \frac{\text{horizontal speed of car}}{\text{vertical speed of snow}}\]we find the angle \(\theta\). Employing an inverse tangent function gives us the precise angle, here calculated as approximately 60.07 degrees. This angle represents how much the path of the snowflakes deviates from the vertical line, as seen from the moving car.