You’re standing outside on a windless day when raindrops begin to fall straight down. You run for shelter at a speed of 5.2 , 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?
v=5.2/tan30 = 9m/s
To find the vertical speed of the raindrops, we can use trigonometry.
Let's consider the raindrops falling at an angle of 30° from the vertical. The vertical speed of the raindrops can be represented by the component of their velocity that is directed downwards.
Given that you are running at a speed of 5.2 m/s, this horizontal speed does not affect the vertical speed of the raindrops. Therefore, we can ignore it for this calculation.
The vertical component of the raindrop's velocity can be determined using the equation:
Vertical Speed = Overall Speed × sin(Angle)
Vertical Speed = 5.2 m/s × sin(30°)
Using a calculator:
Vertical Speed = 5.2 m/s × 0.5
Vertical Speed ≈ 2.6 m/s
Therefore, the vertical speed of the raindrops is approximately 2.6 m/s.
To find the vertical speed of the raindrops, we need to use the concept of vector addition.
Let's break down the motion of the raindrops into vertical and horizontal components. The vertical component is the speed at which the raindrops fall vertically downwards, and the horizontal component is the speed at which the raindrops appear to move horizontally due to your own motion.
Given that the raindrops appear to fall at an angle of 30 degrees from the vertical, we can calculate the horizontal component (your running speed) using trigonometry.
Horizontal component = Speed * cos(angle)
Horizontal component = 5.2 * cos(30)
Horizontal component = 5.2 * √3/2
Horizontal component ≈ 4.5
Since there is no wind and no horizontal motion in reality, the actual horizontal speed of the raindrops is 0.
Now, to find the vertical speed, we can subtract the horizontal component from the overall speed of the raindrops.
Vertical speed = Overall speed - Horizontal component
Vertical speed = 5.2 - 4.5
Vertical speed ≈ 0.7
Therefore, the vertical speed of the raindrops is approximately 0.7 units (the units are not specified in the question, so we assume they are consistent).