While driving north at 25 m/s during a rainstorm you notice that the rain makes an angle of 38° with the vertical. While driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. From these observations, determine the speed and angle of the raindrops relative to the ground.

Verified step by step guidance

1. Identify the frame of reference for each observation. In the first observation, the frame of reference is moving north at 25 m/s, and in the second observation, it is moving south at the same speed.
2. Analyze the first observation where the rain makes an angle of 38° with the vertical. Use vector addition to combine the velocity of the rain relative to the ground (unknown) with the velocity of the car (25 m/s north) to match the observed angle of the rain.
3. In the second observation, the rain appears to fall straight down when the car is moving south at 25 m/s. This suggests that the horizontal component of the rain's velocity relative to the ground is equal to the car's speed but in the opposite direction.
4. Set up equations to solve for the horizontal and vertical components of the rain's velocity. Use trigonometric relationships involving the tangent of the angle (38°) observed in the first scenario to relate the horizontal and vertical components.
5. Solve the system of equations to find the magnitude of the rain's velocity relative to the ground and the angle it makes with the vertical.