The driver notices that the rain leaves no trace on the back windshield of his car slanted at a 60°
angle to the horizontal when the car is moving faster than 30 km per hour. Find the velocity of rain
droplets.
wouldn't arc tan rainvelocity/carvelocity
To find the velocity of rain droplets, we need to analyze the forces acting on them. In this scenario, we know that the rain droplets are falling vertically and the windshield of the car is slanted at a 60° angle to the horizontal.
Let's consider the forces acting on a rain droplet. The two main forces at play are gravity (acting vertically downward) and the resistance force due to the motion of the car (acting horizontally).
When the car is moving faster than 30 km per hour, the resistance force (due to the horizontal motion of the car) becomes large enough to counteract the force of gravity on the rain droplets. As a result, the droplets do not leave any trace on the back windshield.
To find the velocity of the rain droplets, we can equate the force due to gravity with the resistance force:
Force of Gravity = Resistance Force
The force due to gravity can be calculated using the equation:
Force of Gravity = mass of the rain droplet * gravitational acceleration
The resistance force can be calculated using the equation:
Resistance Force = drag coefficient * air density * (velocity of rain droplet)^2 * area of rain droplet
Here, the drag coefficient, air density, and area of the rain droplet are constants.
Since the forces are equal, we can equate the two equations:
mass of the rain droplet * gravitational acceleration = drag coefficient * air density * (velocity of rain droplet)^2 * area of rain droplet
We can then solve this equation to find the velocity of the rain droplets.
Please note that without knowing the specific values for the mass of the rain droplet, gravitational acceleration, drag coefficient, air density, and area of the rain droplet, we cannot provide a specific numerical answer. However, you can use this equation with the appropriate values to calculate the velocity of the rain droplets in this specific scenario.