# vector problem

a boat needs to travel south at a speed of 20kmh-1 however a constant current of 6kmh-1 is flowing from the south-east use vector subtraction to find the equvilant speed in still water for the boat to achieve the actual speed of 20kmh-1 and find the direction in which the boat must head compensate for the current

 Chic_Bowdrie Posts: 54, Reputation: 31 Junior Member #2 May 5, 2012, 09:25 PM
Quote:
 Originally Posted by salsabil a boat needs to travel south at a speed of 20kmh-1 however a constant current of 6kmh-1 is flowing from the south-east use vector subtraction to find the equvilant speed in still water for the boat to achieve the actual speed of 20kmh-1 and find the direction in which the boat must head compensate for the current
I will use the component method. Picture south going from left to right on your monitor. Against a current of 6 km/h from the south east, the boat needs to head slightly to the east of south and travel faster than 20 km/h. The vector representing that heading will intersect the tail of the southeasterly vector whose head joins the head of the vector going south at 20 km/h. The magnitude of the heading vector equals the square root of [20 + 6*cos(pi/4)]^2 + [6*sin(pi/4)]^2 which is 24.611 km/h. The sin of the angle of southeasterly heading is
6*sin(pi/4)/24.611 which corresponds to an angle of about 9.93 degrees east of south. 6*cos(pi/4) is the x component of the extension of the southern resultant vector and 6*sin(pi/4) is the eastern component of the heading vector. This is the best I can do without a diagram.