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 m/s , and you notice while you’re running that the raindrops appear to be falling at an angle of about 30 degrees from the vertical. What’s the vertical speed of the raindrops?
To determine the vertical speed of the raindrops, we need to first understand the horizontal and vertical components of your motion as you run for shelter.
Given that you are running at a speed of 5.3 m/s, we can separate this velocity into its horizontal and vertical components using trigonometry.
The horizontal component of your velocity remains constant since you are running in a straight line. This means that the horizontal component of your velocity is 5.3 m/s.
The vertical component of your velocity can be determined using the angle at which the raindrops appear to fall. In this case, the angle is 30 degrees from the vertical. Since the raindrops appear to be falling straight down, their vertical velocity matches yours.
To find the vertical component of your velocity, we can use the formula:
Vertical component = Velocity * sin(angle)
Using the given values, we can calculate the vertical component of your velocity:
Vertical component = 5.3 m/s * sin(30 degrees)
Now we use the trigonometric function of sine (sin) to calculate:
Vertical component = 5.3 m/s * 0.5
Vertical component = 2.65 m/s
So, the vertical speed of the raindrops is 2.65 m/s.