In a harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat ?
Given: In a harbor, speed of wind is 72 kmh -1 , the flag on the mast of a boat anchored in the harbor flutters along the N-E direction and the boat starts moving at a speed of 51 kmh -1 to the north.
When the boat is anchored, the flag is fluttering in the north-east direction. Hence, wind is blowing toward the north-east direction. When the ship begins sailing toward the north, the flag will move along the direction of the relative velocity of the wind with respect to the boat.
The angle between wind speed and boat is given as,
θ = 90 ° + 45 ° = 135 °
The angle between wind speed and relative velocity of the wind with respect to the boat is given as,
tan β = v b sin θ v w + v b cos θ
Where, the speed of boat is v b and the speed of wind is v w .
By substituting the given values in the above expression,
tan β = 51 sin 135 72 + 51 cos 135 = 51 × 1 2 72 + 51 × ( − 1 2 ) = 51 72 2 − 51 = 1.0038
Further solving for β , we get
β = tan − 1 ( 1.0038 ) = 45.11 °
Angle with respect to east direction is
45.11 ° − 45 ° = 0.11 ° .
Thus, the flag will flutter almost due east.
Given: In a harbor, speed of wind is
When the boat is anchored, the flag is fluttering in the north-east direction. Hence, wind is blowing toward the north-east direction. When the ship begins sailing toward the north, the flag will move along the direction of the relative velocity of the wind with respect to the boat.
The angle between wind speed and boat is given as,
The angle between wind speed and relative velocity of the wind with respect to the boat is given as,
Where, the speed of boat is
By substituting the given values in the above expression,
Further solving for
Angle with respect to east direction is
Thus, the flag will flutter almost due east.
