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|=√(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|=√(20^2+25^2)\\\\\therefore v_1=32.0156units`

Similarly for car 2 we have

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

Therefore

`|v_2|=√(30^2)\\\\\therefore v_2=30.0units`

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