Question

Typhoon Seroja is estimated to be 100.0 km SE of Jakarta as of 4 AM today. At 5 Am, it will be moving 50.0 km W before moving 60.0 km 40OW of N. At 10 AM, it will be heading 40.0 km 30O N of W and at 5 pm, it will be moving 20.0 km N. Solve for the % difference between your answers (Use the

magnitude of VR obtained from both methods)

Answer 1

As we see from the diagram, the magnitude of V_R is 50 km 15° N of W.

Find the magnitude and direction of the displacement vector by the component method:

$$V_E=100\cos45°-50-60\sin40°-40\cos30°+0=\\ =-52.5\text{ km}.\\\space\\ V_N=-100\sin45°+0+60\cos40°+40\sin30°+20=\\ =15.3\text{ km}.\\\space\\ V_R=\sqrt{V_E^2+V_N^2}=54.7\text{ km},\\\space\\ \theta=\arctan\bigg|\frac{V_N}{V_E}\bigg|=16.2°\text{ N of W}.$$

Find the difference in magnitude:

$$\epsilon=\frac{|V_{Rd}-V_R|}{V_R}·100\%=8.6\%$$