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In physics, the concept of relative velocity refers to the measurement of the velocity of an object as perceived from another moving object's frame of reference. It's a cornerstone in understanding motion because it helps us see how speed and direction can change based on an observer's own movement.

When dealing with problems involving relative velocity, it's important to keep in mind the principle of vector addition. For instance, if you're in a moving car and you see raindrops hitting the window, it seems like the rain is coming at an angle. This angle is the result of the vector addition of two velocities: the velocity of the rain and the velocity of the car. This combination gives us a new velocity vector that characterizes the rain's motion relative to the vehicle.

Think about passengers sitting side by side on a train. One throws a ball to the other. To them, the ball might seem to move in a straight line, but to an outside observer, the ball is covering more distance because the train is also moving. Similarly, for the car and rain problem, just as the train changes the ball's apparent path, the car's movement affects how the rain's path is perceived by someone inside the car.

Vector components are essential for comprehending any physical scenario in which directions play a role. A vector, which represents quantities that have both magnitude and direction (like velocity), can be broken down into perpendicular components, usually along the axes of a coordinate system, such as horizontal (x-axis) and vertical (y-axis).

In the case of our car and rain problem, we consider the raindrop's velocity as a vector that has both a horizontal component (caused by the movement of the car) and a vertical component (the rain's actual downward speed). By splitting the raindrop's velocity into these components, we can analyze the problem more easily. For example, in a simple right-angled triangle model, the car's velocity gives us the horizontal component, and using trigonometry, we can determine the rain's vertical component from the given angle of 60 degrees with the vertical.

Trigonometry is crucial in physics for understanding situations where angles and distances are involved. It helps us resolve forces, velocities, and other vector quantities into their components.

In our exercise, the use of trigonometric functions becomes clear through the tangent of the angle formed by the raindrop's trajectory and the vertical. The tangent of 60 degrees provides a ratio that links the horizontal and vertical components of the rain's velocity. Specifically, when rain strikes the car window at a 60-degree angle, we can write the equation \( tan(60^°) = \frac{{V_{rain_{vertical}}}}{{V_{car}}} \), allowing us to solve for the vertical component of the rain's velocity with respect to the car. Such relationships are vital because they enable us to translate an observed phenomenon into a mathematical form that can be analyzed and solved.