Word Problems involving the bearing (direction) of a boat
Word Problems involving the bearing (direction) of a boat
A boat is travelling at a speed of 30 mph. The vector that represents the velocity is 15<√2, -√2>.
What is the bearing of the boat?
SOLUTION:
Graphical solution:
- Construct a vector with components (√2, -√2) .
- Geometrically, multiply the vector by a real number 15. Since it's the positive real number all that does is it stretches the vector out but it still stays pointing in that exact same direction as the original vector w. The result is a new vector .
- Make a right triangle with OAC.
- The tangent of α, is the ratio of the length of the opposite leg to the length of the adjacent leg.
- Calculate the bearing of the boat.