1) Distance: 9 blocks
2) Displacement: 4.12 blocks at [tex]76^{\circ}[/tex] north of east
Explanation:
1)
Distance is a scalar quantity that represents the total length of the path covered by a body during its motion, regardless of its direction. It can be calculated by simply adding the length of each part of the path.
In this problem, the motion of the person is:
4 blocks north
3 blocks east
2 blocks west
Therefore, the distance covered is just the sum of the length of each path:
distance = 4 + 3 + 2 = 9 blocks
2)
Displacement is a vector quantity connecting the initial position to the final position of the motion of a body. Since it is a vector, it has both a magnitude and a direction.
The magnitude can be computed by calculating the distance in a straight line between the initial and final position of motion.
In this problem, we have:
- The final position along the north-south direction is 4 blocks north
- The final position along the east-west direction is
(3 east) + (2 west) = 1 block east
Therefore, the magnitude of the displacement is given by Pythagorean's theorem:
[tex]displacement = \sqrt{4^2 + 1^2}=4.12[/tex] blocks
and the direction is given by
[tex]\theta=tan^{-1}(\frac{4}{1})=76^{\circ}[/tex] north of east.
Learn more about distance and displacement:
brainly.com/question/3969582
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