You’re standing outside on a windless day when raindrops begin to fall straight down. You run for shelter at a speed of 5.3 , and you notice while you’re running that the raindrops appear to be falling at an angle of about 30 from the vertical. What’s the vertical speed of the raindrops?
tan 30 = Vy/Vx = 0.5773
Solve for Vy
Vx is the speed she runs.
You need to learn to provide dimensions along with your numbers. You omitted m/s and degrees.
To find the vertical speed of the raindrops, we need to analyze the motion from two perspectives: the observer (you) and the raindrops.
From your perspective, you are running horizontally at a speed of 5.3 m/s. Since the raindrops appear to be falling at an angle of about 30 degrees from the vertical, this means the raindrops have a horizontal component of motion due to your own velocity.
To determine the vertical component of the raindrop's motion, we can use trigonometry. The vertical speed (V_vertical) can be calculated using the equation:
V_vertical = V_raindrop * sin(angle)
where V_raindrop is the total speed of the raindrop (which we want to find) and angle is the angle of motion with respect to the vertical (30 degrees in this case).
Now, we need to find V_raindrop. Since you, the observer, are moving horizontally, the horizontal component of your velocity affects the apparent motion of the raindrops. The horizontal component of your velocity (V_horizontal) is given by:
V_horizontal = V_observer * cos(angle)
where V_observer is your speed (5.3 m/s) and angle is again the angle of motion with respect to the vertical (30 degrees in this case).
Now, let's find V_horizontal:
V_horizontal = 5.3 m/s * cos(30 degrees)
= 5.3 m/s * √3/2
≈ 4.60 m/s
Since the raindrops appear to be falling straight down to you when you are moving horizontally at 4.60 m/s and the raindrops' vertical speed is unknown, we can use vector addition to find the total speed of the raindrops.
Using Pythagoras' theorem, the total speed (V_raindrop) can be calculated as:
V_raindrop = √(V_horizontal^2 + V_vertical^2)
Now, let's rearrange the equation to find V_vertical:
V_vertical^2 = V_raindrop^2 - V_horizontal^2
Plugging in the values we already know:
V_vertical^2 = V_raindrop^2 - (4.60 m/s)^2
To get the vertical speed, we need to take the square root of both sides:
V_vertical = √(V_raindrop^2 - (4.60 m/s)^2)
However, without knowing the value of V_raindrop, we cannot calculate the exact vertical speed.