question #4\nreference q.46915\nvector a is 12m/s north and vector b is 15m/s east. what is the addition of…

Explanation:

Step1: Recall vector - addition formula for perpendicular vectors

For two perpendicular vectors $\vec{A}$ and $\vec{B}$, the magnitude of the resultant vector $\vec{R}$ is given by $R=\sqrt{A^{2}+B^{2}}$ (Pythagorean theorem for vectors), where $A$ is the magnitude of $\vec{A}$ and $B$ is the magnitude of $\vec{B}$. Here, $A = 12m/s$ and $B=15m/s$.

Step2: Calculate the magnitude of the resultant vector

$R=\sqrt{12^{2}+15^{2}}=\sqrt{144 + 225}=\sqrt{369}\approx19.2m/s$.

Step3: Calculate the direction of the resultant vector

The direction $\theta$ of the resultant vector with respect to the east - direction (using trigonometry, $\tan\theta=\frac{A}{B}$). $\tan\theta=\frac{12}{15}=0.8$, so $\theta=\arctan(0.8)\approx38.7^{\circ}$ North of East.

Answer:

The magnitude of the resultant vector is approximately $19.2m/s$ and the direction is approximately $38.7^{\circ}$ North of East.