Rain is falling steadily but there is no wind. You are in an automobile that moves on a straight, flat highway at a constant speed of 80 km/hr. You see from the drops on the side window that the rain is falling at an angle of 58° measured from vertical (relative to the car). What is the vertical velocity of the raindrops?
Well, if the raindrops are falling at an angle of 58° relative to the car which is moving at a constant speed of 80 km/hr, then I'd say the vertical velocity of the raindrops is probably feeling a bit left out and lonely. It's like the raindrops are trying to wave hello, but the wind is playing hooky. Nevertheless, let's do some calculations to figure it out!
To find the vertical velocity, we need to break down the rain's motion into its horizontal and vertical components. Since the car is moving horizontally and the rain is falling at an angle, we can use some trigonometry to solve this problem.
The vertical velocity of the raindrops can be found by using the equation:
Vertical Velocity = Raindrop Velocity x sin(58°)
Now, since we don't know the exact velocity of the raindrops, we'll have to work with the information given. Let's assume the raindrop velocity is equal to the car's speed, which is 80 km/hr.
Vertical Velocity = 80 km/hr x sin(58°)
But wait a minute, we need to convert the kilometers per hour into meters per second! Let's do some unit conversions:
80 km/hr x (1000 m / 1 km) x (1 hr / 3600 s) = 22.22 m/s
Alright, now let's plug that value back into the equation:
Vertical Velocity = 22.22 m/s x sin(58°)
And using my trusty calculator, the vertical velocity of the raindrops is approximately 18.65 m/s.
So, to sum it all up, the raindrops falling vertically have a vertical velocity of approximately 18.65 m/s. Just remember, they might be a little bummed out without any wind to fluff up their hair, but they're doing their best in the downward direction!
To find the vertical velocity of the raindrops, we need to use trigonometry.
Since the rain is falling at an angle of 58° measured from vertical (relative to the car), we can consider this angle as the angle of depression.
Given that the car is moving at a constant speed of 80 km/hr and there is no wind, we can assume that the vertical velocity of the raindrops will be the same as the velocity of the car.
First, we need to convert the velocity of the car from km/hr to m/s:
80 km/hr = 80,000 m/3600 s ≈ 22.22 m/s
Now, we can calculate the vertical velocity of the raindrops using trigonometry. The vertical velocity (Vv) is given by the formula:
Vv = V * sin(θ)
where V is the velocity of the car and θ is the angle of depression.
Substituting the values into the formula:
Vv = 22.22 m/s * sin(58°)
Using a calculator, we find:
Vv ≈ 18.21 m/s
Therefore, the vertical velocity of the raindrops is approximately 18.21 m/s.
To determine the vertical velocity of the raindrops, we first need to understand the motion of the car and the raindrops relative to each other.
Since there is no wind, we can assume that the raindrops are falling vertically relative to the ground. However, due to the car's motion, they appear to be falling at an angle when observed from inside the car.
By analyzing the given information, we can conclude that the raindrops' vertical velocity relative to the car must be equal to the car's vertical velocity relative to the ground. This is because both the car and the raindrops are affected by gravity.
Therefore, the vertical velocity of the raindrops is the same as the car's velocity, which is 80 km/hr. However, we need to convert this value to meters per second (m/s) to use in subsequent calculations.
To convert from kilometers per hour (km/hr) to meters per second (m/s), we need the following conversion factors:
1 km = 1000 m
1 hr = 3600 s
Applying these conversion factors:
80 km/hr = (80 × 1000 m) / (1 × 3600 s) = 22.22 m/s
Hence, the vertical velocity of the raindrops is 22.22 m/s.