Answer:
First, let's define our coordinates.
Let's call East as the positive x-axis and North as the positive y-axis.
Now the data that we have is:
Speed = 4 mph
Time = 3 hours.
Then the total distance traveled is:
D = 4mph*3h = 12 miles.
We also know that the angle is S 35° E.
(from east, 35° to south)
So we can write this angle as -35°.
Then if we want to know the component in South and East, we can first think this in polar coordinates
(R, θ)
where R = 12 miles, and θ = -35°
Now with this, we have that:
X = R*cos(θ) = the displacement to the east.
Y = R*sin(θ) = the displacement to the north (then -Y is the displacement to the south).
Then we have:
X = 12mi*cos(-35°) = 9.83mi
Y = 12mi*sin(-35°) = - 6.89 mi.
Then:
The displacement to the East is X = 9.83 miles
The displacement to the South is -Y = 6.89 miles.
