Answer to Question #246534 in Physics for Amir

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. Find its VR using both the head-to-tail and component methods.

Answer 1

The component method:

$$V_E=100\cos45°-50-60\sin40°-40\cos30°+0=\\ =-52.5\text{ km}.\\\space\\ V_N=100\sin45°+0+60\cos40°+40\sin30°+20=\\ =157\text{ km}.\\\space\\ V_R=\sqrt{V_E^2+V_N^2}=166\text{ km},\\\space\\ \theta=\arctan\frac{|V_E|}{V_N}=18.5°\text{ N of E}$$