Question

find the resultant of two velocities 3m/s along east and 4m/s along north​

Answer 1

Answer:

The Answer is 5. Either we use Head- tail method or Parallelogram law the answer will be same. Using Parallelogram law we can also find out its direction.

Answer 2

To find:

The resultant of two velocities 3m/s along east and 4m/s along north.

Calculation:

First of all , look at the attached diagram to understand the Velocity vectors and their directions.

Now, the resultant of the velocity vector can be calculated with the help of Pythagora's Theorem as follows:

$\therefore\: | \vec{r}| = \sqrt{ {4}^{2} + {3}^{2} }$

$= > | \vec{r}| = \sqrt{ 16 + 9}$

$= > | \vec{r}| = \sqrt{25}$

$= > | \vec{r}| = 5 \: m {s}^{ - 1}$

Now , let angle between r and 3 m/s vector be $\theta$.

$\therefore\:\cos( \theta) = \dfrac{3}{5}$

$= > \theta = { \cos}^{ - 1} ( \dfrac{3}{5} )$

$= > \theta = {53}^{ \circ }$

So, the resultant vector will be 5 m/s directed 53° North of East.