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

Solution

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:

$\theta=\tan ^{-1}(\frac{44.91}{49.29})=42.33º$

the answer is:

67 knot and 42º