A man walking on a road at 3km/hr encounters rain falling vertically at 18km/hr. At what angle should he hold the umbrella to protect himself from rain?
Worst ans ever ???!!!!
To find the angle at which the man should hold the umbrella, we need to consider the relative velocity between the raindrops and the man.
Step 1: Calculate the relative velocity of the raindrops with respect to the man.
The relative velocity is the vector sum of the velocities of the man and the raindrops. In this case, both velocities are given in km/h, so we can subtract the magnitude of the man's velocity (3 km/h) from the magnitude of the rain's velocity (18 km/h) to find the relative velocity.
Relative velocity = 18 km/h - 3 km/h
Relative velocity = 15 km/h
Step 2: Convert the relative velocity from km/h to m/s.
It's easier to work with the relative velocity in meters per second (m/s), so we need to convert it. To convert from km/h to m/s, divide the velocity by 3.6.
Relative velocity (m/s) = 15 km/h / 3.6
Relative velocity (m/s) ≈ 4.17 m/s
Step 3: Find the angle at which the man should hold the umbrella.
Since the rain is falling vertically downwards, the angle of the umbrella should be such that it counteracts the horizontal component of the relative velocity of the raindrops. The horizontal component is given by the equation:
Horizontal component = Relative velocity * cos(angle)
Rearranging the equation, we can solve for the angle:
Angle = arccos(Horizontal component / Relative velocity)
In this case, the horizontal component is equal to the magnitude of the relative velocity, because the angle we're interested in is the one where the horizontal component cancels out the relative velocity. Thus, the equation becomes:
Angle = arccos(Relative velocity / Relative velocity)
Angle = arccos(1)
Angle = 0 degrees
Therefore, the man should hold the umbrella directly above his head (i.e., at 0 degrees) to protect himself from the rain.