To solve this problem, we need to use vector addition to combine the velocities of the ship and the Gulf Stream. The resulting velocity will be the speed and direction at which the ship will travel.
Let's assume that the ship is traveling due east (i.e., in the direction of the positive x-axis), and the Gulf Stream is flowing due north (i.e., in the direction of the positive y-axis). We can represent the ship's velocity as:
vship = 32 km/hr i
where i represents the unit vector in the x-direction.
We can represent the Gulf Stream's velocity as:
vgulf = 6.4 km/hr j
where j represents the unit vector in the y-direction.
To determine the resulting velocity, we can add the two vectors:
vresultant = vship + vgulf
Using vector addition, we get:
vresultant = (32 km/hr i) + (6.4 km/hr j)
To find the magnitude and direction of the resulting velocity, we can use the Pythagorean theorem and trigonometry. The magnitude of the resulting velocity is given by:
|vresultant| = sqrt((32 km/hr)^2 + (6.4 km/hr)^2) = 32.8 km/hr (rounded to one decimal place)
The direction of the resulting velocity can be found using the inverse tangent function:
theta = arctan(6.4 km/hr / 32 km/hr) = 11.3 degrees north of east (rounded to one decimal place)
Therefore, the ship will travel at a speed of 32.8 km/hr, at an angle of 11.3 degrees north of east, when traveling along the Gulf Stream.