Answer:
Direction of the boat is 43.05° and the speed is 21.66 knot
Step-by-step explanation:
yacht speed = 20 knots
yacht bearing = 185° = 85° below the negative horizontal x-axis
wind speed = 15 knots
wind bearing = 290° = 20° above the negative horizontal x-axis
we find the x and y components of the boat velocities
for yacht,
x component = -20 cos 85° = -1.74 knots
y component = -20 sin 85° = -19.92 knots
for the wind,
x component = -15 cos 20° = -14.09 knots
y component = 15 sin 20° = 5.13 knots
total x component Vx = -1.74 + (-14.09) = -15.83 knots
total y component Vy = -19.92 + 5.13 = -14.79 knots
Resultant speed of the boat = [tex]\sqrt{Vx^{2} + Vy^{2} }[/tex]
==> [tex]\sqrt{15.83^{2} + 14.79^{2} }[/tex] = 21.66 knot
direction of boat = [tex]tan^{-1} \frac{Vy}{Vx}[/tex]
==> [tex]tan^{-1} \frac{14.79}{15.83}[/tex] = 43.05°
