Assume that the Grand Bahama Island lies at the origin of the coordinate systemshown in the diagram at below. Vector vec(A) represents the hurricane’s displacementat 44.5kmh and vector vec(B) represents its displacement after it shifts course threehours later and proceeds at a speed of 22.5kmh. Vector vec(R) represents thehurricane’s displacement after a total time of 4.15 h .(i)Vector vec(A) in the diagram has components to the west and to the north in thiscoordinate system while vector vec(B) has only a north component. During the firstthree hours after passing the island, the displacement of the hurricane isrepresented by vector vec(A), and the storm travels a distance that is the magnitude ofvec(A). This distance isA=v1Δt1=(,kmh)(,h)=,kmand the associated vector vec(A) is in a direction 60.0°north of west.

Answer

Vector Displacement of a Hurricane from Grand Bahama Island

By analyzing a hurricane’s path using vectors, we can estimate its final displacement from the origin (Grand Bahama Island). The motion is broken into two segments with known speeds, directions, and time durations.

🔹 Step 1: First Displacement Vector A

• Speed: 44.5 km/h
• Time: 3.00 h
• Direction: 60.0° north of west

🔹 Step 2: Second Displacement Vector B

• Speed: 22.5 km/h
• Time: 1.15 h
• Direction: Due North

🔹 Step 3: Resultant Displacement Vector R

📊 Summary Table

✅ Conclusion

The hurricane’s total displacement from Grand Bahama Island is approximately 156.48 km at an angle of 64.79° north of west, calculated through vector addition using trigonometric methods.