Question

a delivery truck travels 18 blocks north, 10 blocks east, and 16 blocks south. what is the distance traveled and displacement. ​

Answer 1

1) Distance: 44 blocks

2) Displacement: 10.2 blocks at $11.3^{\circ}$ north of east

Explanation:

1)

- Distance is a scalar quantity that gives a measure of the total length of the path travelled by an object, regardless of its direction

- Displacement is a vector quantity which connects the initial position to the final position of motion of the object. Being a vector, it has both magnitude and direction: the magnitude is the shortest distance between initial and final position, while the direction goes from the initial to the final position.

In this problem, the motion is:

18 blocks north

10 blocks east

16 blocks south

So, the distance is the sum of the distances covered in each part:

distance = 18 + 10 + 16 = 44 blocks

2)

The displacement can be calculated by evaluating the initial and the final position. Along the north-south direction, the displacement is

$d_y = 18 (n) - 16 (s) = 2$ blocks north

Along the east-west direction,

$d_x=10$ blocks east)

So, the magnitude of the displacement is given by Pythagorean's theorem

$d=\sqrt{d_x^2+d_y^2}=\sqrt{2^2+10^2}=10.2$ blocks

And the direction is given by

$\theta=tan^{-1}(\frac{d_y}{d_x})=tan^{-1}(\frac{2}{10})=11.3^{\circ}$

measured as north of east.

Learn more about distance and displacement:

brainly.com/question/3969582

#LearnwithBrainly