Question

5. A yacht is cruising at 20 knots at bearing of 185° when a 15 knot wind starts to blow at a bearing of 290°. Find the direction and speed of the boat.

Answer 1

Direction of the boat is 43.05° and the speed is 21.66 knot

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 =
`\sqrt{Vx^(2) + Vy^(2) }`

==>
`\sqrt{15.83^(2) + 14.79^(2) }` = 21.66 knot

direction of boat =
`tan^(-1) (Vy)/(Vx)`

==>
`tan^(-1) (14.79)/(15.83)` = 43.05°