1) Distance: 44 blocks
2) Displacement: 10.2 blocks at [tex]11.3^{\circ}[/tex] 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
[tex]d_y = 18 (n) - 16 (s) = 2[/tex] blocks north
Along the east-west direction,
[tex]d_x=10[/tex] blocks east)
So, the magnitude of the displacement is given by Pythagorean's theorem
[tex]d=\sqrt{d_x^2+d_y^2}=\sqrt{2^2+10^2}=10.2[/tex] blocks
And the direction is given by
[tex]\theta=tan^{-1}(\frac{d_y}{d_x})=tan^{-1}(\frac{2}{10})=11.3^{\circ}[/tex]
measured as north of east.
Learn more about distance and displacement:
brainly.com/question/3969582
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