To determine the magnitude and direction of the velocity of the passenger with respect to the water, we can use vector addition.
Let's break down the velocities into their x and y components:
Velocity of the ferryboat relative to the water:
Vf_x = 4.40 m/s * cos(28°) (east)
Vf_y = 4.40 m/s * sin(28°) (north)
Velocity of the passenger relative to the boat:
Vp_x = 2.20 m/s (east)
Vp_y = 0 m/s (north)
Now, we can add the components to find the resultant velocity of the passenger relative to the water:
Vr_x = Vf_x + Vp_x
Vr_y = Vf_y + Vp_y
Vr_x = 4.40 m/s * cos(28°) + 2.20 m/s
Vr_y = 4.40 m/s * sin(28°) + 0 m/s
Calculating the components:
Vr_x = 3.988 m/s (east)
Vr_y = 2.042 m/s (north)
To find the magnitude and direction of the resultant velocity, we can use the Pythagorean theorem and inverse tangent functions:
Magnitude of the velocity:
Vr = sqrt(Vr_x^2 + Vr_y^2)
Direction of the velocity (angle with respect to due east):
θ = atan2(Vr_y, Vr_x)
Calculating the magnitude and direction:
Vr = sqrt((3.988 m/s)^2 + (2.042 m/s)^2)
θ = atan2(2.042 m/s, 3.988 m/s)
After calculating:
Vr ≈ 4.53 m/s (magnitude)
θ ≈ 27.13° (angle)
Therefore, the magnitude of the velocity of the passenger with respect to the water is approximately 4.53 m/s, and the direction is 27.13 degrees north of east.