Respuesta :
The total distance covered by a person is [tex]\boxed{533.3\text{ meter}}[/tex].
Further explanation:
Distance is a scalar quantity that is the total distance covered by an object during its motion.
Displacement is a vector quantity, which is the shortest distance from the initial point to the final point or we can say that how much the object change its position.
Given:
A person walks in a distance [tex]x[/tex] in the north direction and then he turn around and walked [tex]7.00x[/tex] in the south direction. The total displacement of the person from his starting position is [tex]400\text{m}[/tex] south.
Step 1:
First we calculate the value of [tex]x[/tex].
A person walks in a distance [tex]x[/tex] in the north direction and then he turn around and walked [tex]7.00x[/tex] in the south direction.
It means the actual position of person is [tex]6.00x[/tex] in south direction.
It can be mathematically expressed as,
[tex]x-7.00x=-6.00x[/tex]
The displacement is the shorter distance from the initial point to final point.
Therefore, the displacement of the person is [tex]6.00x[/tex].
The given displacement is [tex]400[/tex] south.
Thus the value of [tex]x[/tex] is calculated as,
[tex]\begin{aligned}6.00x&=400\\x&=\dfrac{400}{6.00}\\x&=66.66\end{aligned}[/tex]
The value of [tex]x[/tex] is [tex]66.66[/tex].
Step 2:
Now we calculate the total distance covered by the person.
A person walks in a distance [tex]x[/tex] in the north direction and then he turn around and walked [tex]7.00x[/tex] in the south direction.
It means the total distance covered by the person is the sum of distance covered in north direction and the distance covered in the south direction.
It is mathematically expressed as follows:
[tex]\begin{aligned}d&=x+7.00x\\&=8.00x\end{aligned}[/tex]
Therefore, the distance is as follows:
[tex]d=8.00x[/tex] …… (1)
Substitute [tex]x=66.66[/tex] in the equation (1) to calculate the total distance.
[tex]\begin{aligned}d&=8\times66.66\\&=533.3\end{aligned}[/tex]
Therefore, the total distance covered by the person is [tex]\boxed{533.3\text{ meter}}[/tex].
Learn more:
1. Learn more about to solve the equations for the variable https://brainly.com/question/1682776
2. Learn more about the magnitude of the acceleration for the speeding the phase https://brainly.com/question/1597065
3. Algebraic expression for the word phrase ishttps://brainly.com/question/1600376
Answer details:
Grade: Junior school
Subject: Mathematics
Topic: Direction sense
Keywords: Distance, motion, displacement, distance, direction, position, south direction, north direction, scalar, vector, actual position, initial point, final point.
