Answer:
The blue boat traveled 6.1 km farther west than the green boat
The green boat traveled 10.7 km farther south than the blue boat
Explanation:
The equation for linear uniform speed movement is
X(t) = X0 + v * t
Since we have two coordinates (X, Y) we use
X(t) = X0 + vx * t
Y(t) = Y0 + vy * t
The dock will be the origin of coordinates so X0 and Y0 will be zero. The X axis will be pointing west and the Y axis south.
The blue boat moves with a direction 24° south of west, so it will have speeds:
vxb = 104 * cos(24) = 95 km/h
vyb = 104 * sin(24) = 42.3 km/h
And the green boat:
vxg = 104 * cos(37.7) = 82.3 km/h
vyg = 104 * sin(37.7) = 63.6 km/h
After half hour the boats will have arrived at positions
Xb = 95 * 0.5 = 47.5 km
Yb = 42.3 * 0.5 = 21.1 km
And
Xg = 82.3 * 0.5 = 41.4 km
Yg = 63.6 * 0.5 = 31.8 km
The difference in positions of the boats
47.5 - 41.4 = 6.1 km
31.8 - 21.1 = 10.7 km
