# Math Help - Vector Question

1. ## Vector Question

We are studying Vectors at the moment and I am really confused about this one question. If someone could help me it would be greatly appreciated. Please and thank you.

1. A boat travels in a straight line across a bay from point A to point B, a distance of 20 nautical miles on a bearing of 065o. A tide in the bay moves on a bearing of 105o at 3 knots. If the boat’s speed in still water is 10 knots,

(i) Draw a triangle of velocities showing the information given.

(ii) Find the direction in which the boat must be steered so that it travels along the straight line segment joining A to B.

2. ## Triangle of Velocities

Hello ohsoconfused
Originally Posted by ohsoconfused.
We are studying Vectors at the moment and I am really confused about this one question. If someone could help me it would be greatly appreciated. Please and thank you.

1. A boat travels in a straight line across a bay from point A to point B, a distance of 20 nautical miles on a bearing of 065o. A tide in the bay moves on a bearing of 105o at 3 knots. If the boat’s speed in still water is 10 knots,

(i) Draw a triangle of velocities showing the information given.

(ii) Find the direction in which the boat must be steered so that it travels along the straight line segment joining A to B.
In the attached diagram:

• $_BV_E$ is the velocity of the boat relative to the earth. This is in a direction $065^o$, since that is the direction the boat needs to move.

• $_BV_W$ is the velocity of the boat relative to the water. This is 10 units (knots) in magnitude. Its direction gives the direction in which the boat will need to steer.

• $_WV_E$ is the velocity of the water relative to the earth; in other words, the tide or current at 3 knots in a direction $105^o$.

These vectors are connected by the equation $_BV_W+_WV_E=_BV_E$. Notice two things:

• The order of the letters $B, W, E$ in this equation: they go $B..W + W..E = B..E$, just like a displacement vector equation such as $\vec{AB} +\vec{BC} = \vec{AC}$

• In the diagram, the arrows on the two vectors that are added (that's $_BV_W+_WV_E$) follow one another around the triangle. The resultant, or sum, of these two vectors is the third vector $_BV_E$.

So that's how the diagram is drawn. You'll need to use the Sine Rule to calculate the angle between $_BV_W$ and the North, to give you the bearing that the boat must steer. Can you complete this now?