A boat moves with 30km/h into northwest and the current's speed is 10km/h from the northeast, in which speed will the boat travel ?
+129839 10km/h from the northeast means that the current is flowing at 10km/h at 225°
30km/h into northwest means 30km/h at 135°
So....we have these vectors
< 10 cos 225 , 10 sin 225 > and < 30cos135, 30sin135 >
Add the x components = 10 cos 225 + 30cos135 = [ - 10 - 30] / √2 = -40/√2 = -20√2
Add the y components = 10 sin 225 + 30sin135 = [ - 10 + 30] / √2 = 20 / √2 = 10√2
Speed of boat = √ [ ( -20√2)^2 + ( 10√2)^2 ] = √[ 800 + 200] = √1000 ≈ 31.62 km/ h
Direction = arctan [ -1/2] = -26.57° + 180° = 153.43°
Thanks a lot CPhill, but the problem is that the speed will be 28,3 km/h and I didn't know how to get this answer.
