Answer to Question #251323 in Mechanics | Relativity for JNV

Question

6. An airplane travels 210km on a straight course at an angle 25 degrees east of north. It changes its course by moving 110 km north before reaching its destination. Determine the resultant displacement of the airplane. A.) Use graphical method B.) Use component method.

Answer 1

A) According to graphical method, the displacement is 310 km 70° N of E.

B) Use component method:

$$R_E=210\sin25°=88.7\text{ km},\\ R_N=210\cos25°+110=300\text{ km},\\\space\\ R=\sqrt{R_E^2+R_N^2}=313\text{ km}.\\\space\\ \theta=\arctan\frac{300}{88.7}=73.53°\text{ N of E}.$$