Question

velocity assessment. a woman runs 3.7 miles north and 4.5 miles east. what is her resultant displacement? northwest northeast southeast southwest

Explanation:

Step1: Identify the vectors

The north - south and east - west directions are perpendicular. The north - ward displacement $d_1 = 3.7$ miles (positive y - direction) and the east - ward displacement $d_2=4.5$ miles (positive x - direction).

Step2: Use the Pythagorean theorem

The resultant displacement $d$ of two perpendicular vectors is given by $d=\sqrt{d_1^{2}+d_2^{2}}$. Substitute $d_1 = 3.7$ and $d_2 = 4.5$ into the formula: $d=\sqrt{(3.7)^{2}+(4.5)^{2}}=\sqrt{13.69 + 20.25}=\sqrt{33.94}\approx5.82$ miles.

Step3: Find the direction

The direction $\theta$ of the resultant displacement with respect to the east direction is given by $\tan\theta=\frac{d_1}{d_2}$. So, $\tan\theta=\frac{3.7}{4.5}\approx0.8222$, and $\theta=\arctan(0.8222)\approx39.4^{\circ}$ north of east, which is the northeast direction.

Answer:

Northeast