Solution:

Given:
- Speed of raindrops: 20 m/s
- Speed of the car: 15 m/s
- Inclination angle of the windscreen: 23° to the vertical

To find:
- Angle at which the raindrops fall on the windscreen

Assumptions:
- The car is moving in a straight line with a constant velocity.
- The raindrops are falling straight down vertically.

Analysis:
When the raindrops fall vertically, their velocity vector is purely vertical and has no horizontal component. However, when the car is moving, the raindrops appear to have a slanted trajectory when observed from the frame of reference of the car. This is because the car is moving horizontally while the raindrops are falling vertically.

The velocity of the raindrops relative to the car is the vector sum of their individual velocities. This can be determined using vector addition.

Let's assume the angle at which the raindrops fall on the windscreen is θ.

The vertical component of the raindrop's velocity is given by the speed of the raindrop itself, which is 20 m/s. This can be represented as:
Vertical component of velocity = 20 m/s

The horizontal component of the raindrop's velocity is equal to the horizontal component of the car's velocity, which is 15 m/s. This can be represented as:
Horizontal component of velocity = 15 m/s

Therefore, the velocity of the raindrops relative to the car can be determined using the Pythagorean theorem:
Relative velocity = √[(Vertical component of velocity)^2 + (Horizontal component of velocity)^2]

Substituting the given values:
Relative velocity = √[(20 m/s)^2 + (15 m/s)^2]
Relative velocity ≈ √(400 m^2/s^2 + 225 m^2/s^2)
Relative velocity ≈ √625 m^2/s^2
Relative velocity ≈ 25 m/s

Now, we can use trigonometry to find the angle θ at which the raindrops fall on the windscreen. In a right-angled triangle, the tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, the side opposite to the angle θ is the vertical component of the relative velocity, and the side adjacent to the angle θ is the horizontal component of the relative velocity.

Therefore, the tangent of the angle θ can be calculated as:
tan(θ) = (Vertical component of velocity) / (Horizontal component of velocity)
tan(θ) = 20 m/s / 15 m/s
tan(θ) ≈ 1.333

To determine the angle θ, we need to find the inverse tangent (also known as the arctan) of 1.333. Using a calculator, we find:
θ ≈ arctan(1.333)
θ ≈ 53.13°

Therefore, the raindrops fall on the windscreen at an angle of approximately 53.13° with respect to the horizontal.