Question

A boat is traveling at 54 knots in a direction of 48°. It encounters wind moving at 14 knots in a direction of 20°. What is the true velocity and direction of the boat? Round to the nearest whole number.

Answer 1

For this case we have two vectors given:

54 knots 48º

14 knots 20º

Therefore we can find the resultant vector like this:

`F_x=54\cdot\cos 48+14\cdot\cos 20=36.13+13.15=49.29`
`F_y=54\sin 48+14\cdot\sin 20=40.13+4.79=44.91`

Therefore the magnitude is:

`F=\sqrt[]{(49.29)^2+(44.91)^2}=66.68`

and the angle is given by:

`\theta=\tan ^(-1)((44.91)/(49.29))=42.33º`

the answer is:

67 knot and 42º