Answer to Question #335170 in Trigonometry for math

Question

A ship captain is plotting a course to an island 80 km SW of his current position.

The wind is blowing from the East at 15 km/h. What must the velocity vector of

the ship be in order for it to arrive at the island in 2 hours (hint: think about what

the resultant velocity must be).

Answer 1

Resultant velocity is $|v|=\sqrt{|a|^2+|b|^2-2|a||b|cos \alpha}$

$|v|=80/2=40 km/h$

$40=\sqrt{|a|^2+15^2-2|a|x15cos (45)}$

$1600=|a|^2+225-21.3|a|$

$|a|^2-21.3|a|-1375=0$

$D=21.3^2+4x1375=5953.69$

$|a|_1=\frac{21.3+\sqrt{5953.69}}{2}=49.23$

$|a|_2=\frac{21.3-\sqrt{5953.69}}{2}=-27.94<0$

Answer: velocity vector of the ship should be 49.23 km/h to SW.