Question

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.

Answer 1

Answer with explanation:

For any object having the velocity vector as

$\overrightarrow{v}=v_x\widehat{i}+v_y\widehat{j}+v_z\widehat{k}$

the magnitude of velocity is given by

$|v|=\sqrt{v_x^2+v_y^2+v_z^2}$

For car 1 the velocity vector is

$\overrightarrow{v}_1=20\widehat{i}+25\widehat{j}$

Therefore

$|v_1|=\sqrt{20^2+25^2}\\\\\therefore v_1=32.0156units$

Similarly for car 2 we have

$\overrightarrow{v}_2=30\widehat{i}$

Therefore

$|v_2|=\sqrt{30^2}\\\\\therefore v_2=30.0units$

Comparing both the values we find that car 1 has the greater speed.