A car travels due east with a speed of 35.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 70.0° with the vertical. Find the velocity of the rain with respect to the following reference frames.
96.2km/hr
To find the velocity of the rain with respect to different reference frames, we need to use vector addition. We'll start by finding the velocity of the rain with respect to the Earth, and then convert it to the other reference frames.
1. Velocity of the rain with respect to the Earth:
The raindrops are falling vertically with respect to the Earth, so their velocity with respect to the Earth is simply the vertical component of their velocity. We can calculate this using trigonometry.
Given:
- Angle between the raindrops and vertical = 70.0°
- Speed of the car = 35.0 km/h
To find the vertical component of the velocity, we can use the equation:
vertical velocity = raindrop velocity * sin(angle)
= raindrop velocity * sin(70.0°)
Since the angle is measured with respect to the vertical, the vertical component of velocity will be positive. Therefore, the velocity of the rain with respect to the Earth is given by:
velocity of the rain with respect to the Earth = raindrop velocity * sin(70.0°)
2. Velocity of the rain with respect to the car:
To calculate the velocity of the rain with respect to the car, we need to subtract the velocity of the car from the velocity of the rain with respect to the Earth.
velocity of the rain with respect to the car = velocity of the rain with respect to the Earth - velocity of the car
3. Velocity of the rain with respect to an observer standing by the side of the road:
To calculate the velocity of the rain with respect to an observer standing by the side of the road, we need to subtract the velocity of the car from the velocity of the rain with respect to the Earth.
velocity of the rain with respect to the observer = velocity of the rain with respect to the Earth - velocity of the car
Note: In both cases, the angles between the raindrops and the vertical remain the same, hence the vertical component of the velocity remains the same.
By following these steps and using the given values, you can find the velocity of the rain with respect to the desired reference frames.