Wind is blowing at a speed of 70 km/hr and the flag hoisted on a ship in a harbour flutters along N-E direction.if the ship starts moving at a speed of 50 km/hr towards north,what will be the direction of the flag hoisted on the ship?

speed of wind = 70 kmph in NE dir

 

speed of ship = 50 kmph in north dir

 

angle between the two  = 45 degree

thus the flag will now flutter in the direction of their net velocity

thus using parallelogram law of addition of velocities,

 

net V² = 50² + 70² + 2.50.70.cos(45)

and V = 111.12 kmph

and direction = tan^-1[70.cos(45)/(70.sin(45)-50)]

(It can be easily derieved using vector resolution and general use of trigonometry)