Answer:
Ok, the speed is 18 mph.
The angle is 293°, and we usually measure the angles from the x-axis, so we can write our coordinates of velocity as:
Vx = 18mph*cos(293°) = 7mph.
Vy = 18mph*sin(293°) = -16.6mph.
Then we can write this as a vector (Vx, Vy)
Velocity = (7mph, -16.6mph)
Now, for the position, we can integrate over time, and using that the position (0, 0) is the starting point of the ship, we have that the position vector is:
P(t) = (7mph*t, -16,6mph*t)
Where t is the number of hours after the ship leaved the port.
If t = 0 is 0:00pm, then at 3:30pm we have t = 3 hours and 30 minutes
one hour has 60 minutes, then 30 minutes is equivalent to 0.5 hours.
Then 3:30pm we have t = 3.5 houes.
Now we replace this in the position vector and the location of the ship at 3:30pm is:
P(3.5h) = (7mph*3.5h, -16.6mph*3.5h) = (24.5 mi, -58.1 mi)
Where the first component describes the displacement in the x-axis, and the second component describes the displacement in the y-axis.
