A man is walking due east at the rate of of 4kmph and the rain is falling 30° east of vertical with a velocity of 6kmph the velocity of rain relative to the man will be
To find the velocity of the rain relative to the man, we need to consider the vector components of the man's velocity and the rain's velocity.
The man is walking due east at a velocity of 4 km/hr. Since the rain is falling 30° east of vertical, we need to determine the vertical and horizontal components of the rain's velocity.
The vertical component of the rain's velocity can be calculated by multiplying the rain's velocity (6 km/hr) by the sine of the angle:
Vertical component of rain's velocity = 6 km/hr * sin(30°)
Using the value of sin(30°) ≈ 0.5, the vertical component of the rain's velocity is:
Vertical component of rain's velocity = 6 km/hr * 0.5 = 3 km/hr
The horizontal component of the rain's velocity can be calculated by multiplying the rain's velocity (6 km/hr) by the cosine of the angle:
Horizontal component of rain's velocity = 6 km/hr * cos(30°)
Using the value of cos(30°) ≈ 0.866, the horizontal component of the rain's velocity is:
Horizontal component of rain's velocity = 6 km/hr * 0.866 ≈ 5.196 km/hr
Now, let's calculate the velocity of the rain relative to the man. Since both the vertical and horizontal components should be added to the man's eastward velocity, the resulting velocity will have two components: one in the east direction and another in the vertical direction.
Velocity of the rain relative to the man (in the east direction) = eastward velocity of the man + horizontal component of rain's velocity
Velocity of the rain relative to the man (in the east direction) = 4 km/hr + 5.196 km/hr = 9.196 km/hr (approximately)
Velocity of the rain relative to the man (in the vertical direction) = vertical component of rain's velocity
Velocity of the rain relative to the man (in the vertical direction) = 3 km/hr
Therefore, the velocity of the rain relative to the man is approximately 9.196 km/hr in the east direction and 3 km/hr in the vertical direction.
east rain speed = 6 sin 30 = 3 km/h
3-4 = -1 so in his face