Question

If you add two velocity vectors going in opposite directions, will the resultant vector be smaller or larger than the vectors you are adding?
Choose the correct answer with the correct reasoning.

Question 11 options:

smaller, because the vectors are added to each other and increase the velocity


larger, because the vectors are added to each other and increase the velocity


smaller, because part of the velocities cancel each other out


larger, because the part of the velocities cancel each other out

Answer 1

smaller, because the part of the velocities cancel each other out

Answer 2

Explanation:

If two vectors going in opposite directions and we add them, the resultant is given by the sum of vectors as :

$R=\sqrt{A^2+B^2+2AB\ cos(180)}$, cos (180) = -1

$R=A+(-B)$

If the vectors are in same directions, the resultant is equal to the sum of vectors. Here, the resultant of two vectors is smaller because the part of the velocities cancel out each other. Hence, the correct option is (c).