Rain is falling vertically with a speed of 30 m s¯¹. A woman rides a bicycle with a speed of 10 m s¯¹ in the north to south direction. What is the direction in which she should hold her umbrella ?
Given: The velocity of rain falling vertically is 30 ms − 1 and velocity of bicycle is 10 ms − 1 in north to south direction.
The situation can be described as shown in the figure below.
The direction in which the woman holds the umbrella is given by,
tan β = | v c | | v r |
Where, velocity of bicycle is v c and velocity of rain is v r .
By substituting the given values in the above expression, we get
tan β = 10 30 = 1 3 β = tan − 1 ( 1 3 ) = 18 ° 2 6 ′
Thus, the woman must hold the umbrella toward the south, at an angle of 18 ° 2 6 ′ with the vertical.
Given: The velocity of rain falling vertically is
The situation can be described as shown in the figure below.
The direction in which the woman holds the umbrella is given by,
Where, velocity of bicycle is
By substituting the given values in the above expression, we get
Thus, the woman must hold the umbrella toward the south, at an angle of
