A man running horizontal road with velocity 8 km/hr. Find the rain falling vertically downward direction. When he increases speed to 12 km/hr he find rain drops are falling at an angle 30' with downward vertically. What will be the velocity of rain?
could we keep the answer as 4root7?
yes
To find the velocity of rain, we need to consider the man's velocity and the angle at which the rain is falling.
Let's break down the given information:
- When the man is running with a velocity of 8 km/hr, the rain is falling vertically downward.
- When the man increases his speed to 12 km/hr, the rain is falling at an angle of 30' (30 degrees) with the vertical downward direction.
First, let's convert the given velocities to m/s for consistency:
- Velocity of the man running = 8 km/hr = (8 * 1000) m/ (60 * 60) s = 2.22 m/s
- Increased velocity of the man = 12 km/hr = (12 * 1000) m/ (60 * 60) s = 3.33 m/s
Now, we can analyze the situation considering the components of velocity:
1. Rain falling vertically downward:
Since the man is running horizontally, his velocity has no vertical component. Therefore, the velocity of rain in the vertical direction will be equal to 0 m/s.
2. Rain falling at an angle of 30 degrees:
When the rain is falling at an angle of 30 degrees, we will need to consider the horizontal and vertical components of the man's velocity along with the rain's velocity.
Using trigonometry, we can calculate the horizontal and vertical components of the man's velocity:
- Horizontal component: velocity_man * cos(angle)
= 3.33 m/s * cos(30 degrees)
= 3.33 m/s * (√3/2)
≈ 2.88 m/s
- Vertical component: velocity_man * sin(angle)
= 3.33 m/s * sin(30 degrees)
= 3.33 m/s * (1/2)
≈ 1.67 m/s
Since the rain is falling vertically downward, its velocity will have no horizontal component. Therefore, the velocity of rain in the horizontal direction will be equal to 0 m/s.
Finally, we can determine the velocity of rain by adding the horizontal and vertical components:
- Velocity of rain = √(horizontal_component^2 + vertical_component^2)
= √(0^2 + 1.67^2)
≈ 1.67 m/s
Hence, the velocity of rain falling at an angle of 30 degrees when the man's speed increases to 12 km/hr is approximately 1.67 m/s.
How
4.1.732
loose
I am interpreting your first two sentences as meaning:
"A man running horizontally along a road, with velocity 8 km/hr, finds the rain falling in a vertically downward direction."
That statement implies that the rain has a horizontal component of 8 km/hr in the same direction the runner is running. When he runs at the same speed, the rain apears to come straight down.
If he increases his speed to 12 km/hr, there is a 4 km/hr relative velocity of wind into his face. The vertical component of the wind velcity, Vy, must such that 4/Vy = tan 30
Vy = 6.93 km/hr
Vx = 8.00 km/hr
Wind speed (magnitude) = 10.58 km/hr