You're driving on the freeway going 90km per hour and it starts to rain. The raindrops make an angle of 40 degrees with the vertical when viewed through the driver's side window.
What is the speed of the raindrops measured by someone at rest relative to the freeway? What is the speed of the raindrops relative by you?
drop speed relative to rest
... s = 90 kph / tan(40º)
drop speed relative to vehicle
... s = 90 kph / sin(40º)
To calculate the speed of the raindrops measured by someone at rest relative to the freeway, we need to break down the motion into its horizontal and vertical components.
Given information:
- Your driving speed: 90 km/h
- Angle of the raindrops with the vertical: 40 degrees
To find the horizontal component of the raindrops' speed, we can use trigonometry. Since the angle is measured with respect to the vertical, we can use the sine function. The horizontal component of the raindrops' speed is given by:
Horizontal component = Speed of raindrops * sin(angle)
Now, let's find the vertical component of the raindrops' speed. Since the angle is measured with respect to the vertical, we can use the cosine function. The vertical component of the raindrops' speed is given by:
Vertical component = Speed of raindrops * cos(angle)
However, we are interested in the speed of the raindrops measured by someone at rest relative to the freeway. This means we need to subtract the speed of the car (90 km/h) from the horizontal component of the raindrops' speed.
Therefore, the speed of the raindrops measured by someone at rest relative to the freeway is given by the formula:
Speed of raindrops measured by someone at rest = Horizontal component - Speed of the car
To find the speed of the raindrops relative to you (the driver), we simply need to calculate the magnitude of the speed vector of the raindrops. This can be found using the Pythagorean theorem:
Magnitude of the speed vector = √(Horizontal component^2 + Vertical component^2)
So, to summarize:
1. Calculate the horizontal component of the raindrops' speed using the formula: Speed of raindrops * sin(angle).
2. Calculate the vertical component of the raindrops' speed using the formula: Speed of raindrops * cos(angle).
3. Calculate the speed of the raindrops measured by someone at rest relative to the freeway by subtracting the speed of the car from the horizontal component obtained in step 1.
4. Calculate the speed of the raindrops relative to you (the driver) using the magnitude of the speed vector obtained in step 3.
Now you can use these calculations to find the answers to your question.