Question

A delivery truck leaves a warehouse and travels 3.20 km east. The truck makes a right turn and travels 2.45 km south to arrive at its destination. What is the magnitude and direction of the truck’s displacement from the warehouse? Group of answer choices 5.65 km, 52.5° south of east 2.40 km, 45.0° south of east 0.75 km, 37.8° south of east 2.30 km, 52.5° south of east 4.03 km, 37.4° south of east

Answer 1

Explanation:

It is given that,

Displacement of the delivery truck, $d_1=3.2\ km$ (due east)

Then the truck moves, $d_2=2.45\ km$ (due south)

Let d is the magnitude of the truck’s displacement from the warehouse. The net displacement is given by :

$d=\sqrt{d_1^2+d_2^2}$

$d=\sqrt{3.2^2+2.45^2}$

d = 4.03 km

Let $\theta$ is the direction of the truck’s displacement from the warehouse from south of east.

$\theta=tan^{-1}(\dfrac{2.45}{3.2})$

$\theta=37.43^{\circ}$

So, the magnitude and direction of the truck’s displacement from the warehouse is 4.03 km, 37.4° south of east.