Rain falls vertically downward with a velocity of 2.4m/s. A boy moves at a speed of of 6m/s east in a bicycle with an umbrella. What is the velocity of the rain with the respect to the boy. What angle from horizontal should he hold his umbrella?
sqrt(2.4^2+36)
tan theta = 2.4/6
2.5
To find the velocity of the rain with respect to the boy, we need to use vector addition.
First, let's break down the velocities into their horizontal and vertical components.
Given:
Velocity of rain = 2.4 m/s downward
Velocity of boy = 6 m/s east
The vertical component of the rain's velocity is simply 2.4 m/s downward since rain falls vertically. The horizontal component of the rain's velocity is zero since rain does not move horizontally.
Now, to find the velocity of the rain with respect to the boy, we can subtract the boy's velocity components from the rain's velocity components.
Vertical component: 2.4 m/s - 0 m/s = 2.4 m/s downward
Horizontal component: 0 m/s - 6 m/s = -6 m/s west
So, the velocity of the rain with respect to the boy is 2.4 m/s downward and 6 m/s west.
Now, to determine the angle at which the boy should hold his umbrella, we can use trigonometry. The angle can be found using the tangent function:
tan(angle) = vertical component / horizontal component
tan(angle) = 2.4 m/s / (-6 m/s)
Now, we can take the inverse tangent (arctan) of both sides to find the angle:
angle = arctan(2.4 m/s / (-6 m/s))
Using a calculator, we can determine:
angle ≈ -22 degrees
Therefore, the boy should hold his umbrella at an angle of approximately 22 degrees below horizontal in order to counteract the rain's velocity.