Raindrops falling on a moving car windscreen

To find the angle at which raindrops fall on the windscreen of a car moving at a certain velocity, we need to consider the relative motion of the raindrops with respect to the car. Let's break down the problem step by step:

Given:
- Speed of raindrops (v_rain) = 20 m/s
- Velocity of the car (v_car) = 15 m/s
- Angle of inclination of windscreen (θ) = 23 degrees

Step 1: Finding the relative velocity of raindrops with respect to the car
The raindrops are falling vertically, but due to the motion of the car, they appear to be falling at an angle when observed from the car. We need to find the relative velocity of the raindrops with respect to the car.

The relative velocity (v_rel) can be calculated using vector subtraction:

v_rel = v_rain - v_car

In this case, since the raindrops are falling vertically, the vertical component of the relative velocity (v_rel_y) will be equal to the vertical component of the raindrops' velocity (v_rain_y), and the horizontal component of the relative velocity (v_rel_x) will be equal to the horizontal component of the car's velocity (v_car_x).

Step 2: Finding the angle at which raindrops fall on the windscreen
To find the angle at which the raindrops fall on the windscreen, we need to consider the angle between the relative velocity vector and the vertical direction.

We can use trigonometry to find this angle:

tan(θ') = v_rel_y / v_rel_x

where θ' is the angle between the relative velocity vector and the vertical direction.

Step 3: Calculating the final angle
The final angle at which the raindrops fall on the windscreen will be the sum of the angle of inclination of the windscreen (θ) and the angle between the relative velocity vector and the vertical direction (θ').

θ_final = θ + θ'

Calculations:
1. Relative velocity components:
v_rel_x = v_car = 15 m/s (horizontal component)
v_rel_y = v_rain = 20 m/s (vertical component)

2. Angle between the relative velocity vector and the vertical direction:
θ' = arctan(v_rel_y / v_rel_x)
θ' = arctan(20 / 15) ≈ 53.13 degrees

3. Final angle at which the raindrops fall on the windscreen:
θ_final = θ + θ'
θ_final = 23 + 53.13 ≈ 76.13 degrees

Therefore, the raindrops fall on the windscreen at an angle of approximately 76.13 degrees.

Explanation:
When raindrops fall vertically, they appear to fall at an angle when observed from a moving car due to the car's velocity. The relative velocity of the raindrops with respect to the car can be calculated by subtracting the car's velocity from the raindrops' velocity. The angle at which the raindrops fall on the windscreen can be found by considering the angle between the relative velocity vector and the vertical direction. By adding this angle to the angle of inclination of the windscreen, we