Answer to Question #249074 in Mechanics | Relativity for Mary Jane

Question

Find the Vr of the vectors given below using both the head-to-tail and component methods.

 

An athlete runs 65.0 km SE the proceeds 50.0 km NE before running 45.0 km NW and 60.0 km W.

Scale = 1.0 cm:10 km

Answer 1

By the component method:

$$V_{1S}=65\cos45°=46\text{ km},\\ V_{1E}=65\sin45°=46\text{ km}.\\ V_{2S}=-50\cos45°=-35\text{ km},\\ V_{2E}=50\sin45°=35\text{ km}.\\ V_{3S}=-45\cos45°=-32\text{ km},\\ V_{3E}=-45\sin45°=-32\text{ km}.\\ V_{4S}=60\cos90°=0\text{ km},\\ V_{4E}=-60\sin90°=-60\text{ km}.\\\space\\ V_{rS}=V_{1S}+V_{2S}+V_{3S}+V_{4S}=-21\text{ km},\\ V_{rE}=V_{1E}+V_{2E}+V_{3E}+V_{4E}=-11\text{ km},\\\space\\ V_r=\sqrt{V^2_{rE}+V^2_{rS}}=24\text{ km}.\\\space\\ \theta=\arctan\frac{21}{11}=62°\text{ North of West.}$$