Which is traveling faster, a car whose velocity vector is 201 + 25), or a car whose velocity vector is 30i, assuming that the units are the same for both directions? is the faster car. At what speed is the faster car traveling? speed = Enter the speed as a NUMBER, using exact values or at least 4 decimal place accuracy.

Accepted Solution

Answer with explanation:For any object having the velocity vector as [tex]\overrightarrow{v}=v_x\widehat{i}+v_y\widehat{j}+v_z\widehat{k}[/tex]the magnitude of velocity is given by[tex]|v|=\sqrt{v_x^2+v_y^2+v_z^2}[/tex]For car 1 the velocity vector is[tex]\overrightarrow{v}_1=20\widehat{i}+25\widehat{j}[/tex]Therefore[tex]|v_1|=\sqrt{20^2+25^2}\\\\\therefore v_1=32.0156units[/tex]Similarly for car 2 we have[tex]\overrightarrow{v}_2=30\widehat{i}[/tex]Therefore[tex]|v_2|=\sqrt{30^2}\\\\\therefore v_2=30.0units[/tex]Comparing both the values we find that car 1 has the greater speed.