To find the resultant velocity and direction of the ship, we can use vector addition.
First, we need to convert the velocities into their x and y components:
Ship velocity: 22 knots at 157°
Vx = 22 cos(157°) = -20.41 knots
Vy = 22 sin(157°) = 7.25 knots
Current velocity: 5 knots at 213°
Vx_current = 5 cos(213°) = -3.74 knots
Vy_current = 5 sin(213°) = -2.39 knots
Now, we can add the x components and y components separately to find the resultant velocity:
Vx_resultant = -20.41 knots - 3.74 knots = -24.15 knots
Vy_resultant = 7.25 knots - 2.39 knots = 4.86 knots
Finally, we can find the magnitude and direction of the resultant velocity:
Magnitude of resultant velocity = sqrt((-24.15)^2 + (4.86)^2) = 24.7 knots
Direction of resultant velocity = arctan(4.86 / -24.15) = -11.3° (measured clockwise from the north axis)
Therefore, the resultant velocity of the ship is 24.7 knots at a direction of 348.7°.
A ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157° (knots being a unit used to measure the speed of aircrafts and boats). The current has a velocity of 5 knots along a bearing of 213°. Find the resultant velocity and direction of the ship. (Remember that bearing is measured clockwise from the north axis). (1 point) Responses 25 knots at 166.5° 25 knots at 166.5° 27 knots at 350° 27 knots at 350° 166.5 knots at 25° 166.5 knots at 25° 350 knots at 27°
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