How to solve: If a man walk with speed of 2km/hour and rain fall became in the shape of 90 degree.then find out velocity n direction of rain if man walk with speed of 4km/hour and angle of rain is 45 degree
90 degrees is not a "shape" for rain. Do you mean vertical rain is falling? That would be a slope.
Can you not just copy the problem from the book, so we get the correct wording?
It's enough work to solve the problem for the answer, without having to figure out the question as well!
To solve this problem, we need to break it down into two components: the velocity of the rain relative to the man and the direction of the rain.
First, let's calculate the velocity of the rain relative to the man. We can use vector addition to find the resultant velocity.
1. Start by drawing a diagram to represent the situation. Place the man at the origin (0,0) and draw a line representing his velocity of 4 km/h at an angle of 45 degrees.
2. Next, draw a line representing the rain's velocity of 2 km/h at a 90-degree angle to the man.
3. Using basic trigonometry, we can determine the x-component and y-component of the rain's velocity.
- For the x-component: velocity_rain_x = rain_velocity * cos(rain_angle)
- For the y-component: velocity_rain_y = rain_velocity * sin(rain_angle)
In this case, since the angle of the rain is 90 degrees, the x-component of the rain's velocity will be 0 (velocity_rain_x = 0), and the y-component of the rain's velocity will be 2 km/h (velocity_rain_y = 2 km/h).
4. Now, add the x-components and y-components of the velocities to find the resultant velocity vector:
- Resultant_x = man_velocity * cos(man_angle) + velocity_rain_x
- Resultant_y = man_velocity * sin(man_angle) + velocity_rain_y
Plugging in the values, we have:
- Resultant_x = 4 km/h * cos(45°) + 0 = 2.83 km/h
- Resultant_y = 4 km/h * sin(45°) + 2 km/h = 4.83 km/h
So, the velocity of the rain relative to the man is approximately 2.83 km/h in the x-direction and 4.83 km/h in the y-direction.
Now, let's determine the direction of the rain relative to the man. We can calculate the angle using trigonometry:
1. To find the angle, we use the formula:
Angle = arctan(Resultant_y / Resultant_x)
Plugging in the values, we have:
Angle = arctan(4.83 km/h / 2.83 km/h) ≈ 60.08°
Therefore, the velocity of the rain relative to the man is approximately 7.13 km/h at an angle of 60.08 degrees.