a man moves 2km/hour and rain has started now falling with 2km/hour at what angle should umbrellla be kept so that man can not go wet
depends on the size of the umbrella.
To determine at what angle the umbrella should be kept so that the man does not get wet, we need to consider the vector addition of the man's velocity and the rain's velocity.
First, let's break down the velocities into their x and y components. Since the man's velocity is 2 km/hour, we can say that his velocity in the x direction (horizontal) is 2 km/hour (assuming he is moving directly horizontally). The rain's velocity is also 2 km/hour, but since it is falling vertically, its velocity in the y direction is 2 km/hour.
Now, if the umbrella is held at an angle, we can think of it as providing additional velocity in the y direction to counteract the rain's vertical velocity. Let's assume the umbrella provides a velocity of u km/hour in the y direction.
The total velocity of the rain relative to the man is the vector sum of the man's velocity and the rain's velocity. The magnitude of this velocity should be zero in the y direction to prevent the man from getting wet. Mathematically, we can represent this as:
man's velocity in y direction (0 km/hour) = rain's velocity in y direction (2 km/hour) + umbrella's velocity in y direction (u km/hour)
Therefore, to find the angle at which the umbrella should be kept, we need to determine the value of u.
Since the man's velocity is directly in the x direction, we can ignore it when considering the y direction. Thus, we can rearrange the equation:
0 km/hour = 2 km/hour + u km/hour
Solving for u, we get:
u km/hour = -2 km/hour
The negative sign indicates that the umbrella's velocity in the y direction should cancel out the rain's velocity in the y direction. Therefore, the umbrella should be kept at an angle where its vertical velocity (upward) is 2 km/hour, equal in magnitude but opposite in direction to that of the falling rain.
Note that this explanation assumes the man is standing still; if the man is also moving in the y direction, the calculations would be more complex and dependent on the angle and magnitude of his y-velocity.