Question

A person walks along the path of a rectangle from point P to point R as shown in the below figure
a) Find the distance travelled by the person
b) Find out the magnitude of the displacement of the person​

Answer 1

Answer:

Distance travelled = 7 km

Displacement = 5.38 km

Explanation:

As per the provided information in the given question, we have :

• A person walks along the path of a rectangle from point P to point R.

We are asked to calculate the distance travelled by the person and the magnitude of his displacement.

Distance is the total length of the path covered by the body. Here, the body starts from point P and ends at point R. For reaching at point R, it covers the path PQ and QR. So, distance covered by the body will be given by,

$\longmapsto\rm { Distance = PQ + QR}$

$\longmapsto\rm { Distance = (5 +2) \; km}$

$\longmapsto\bf { Distance = 7 \; km}$

∴ Distance travelled by the body is 7 km.

Now, we have to calculate the magnitude of his displacement.

Displacement is the shortest distance from initial to final position. The shortest distance from initial to final position is always a straight line. Here, initial position of the body is P and final position of the body is R. As the shortest distance from initial to final position is always a straight line, so the displacement of the person is PR. PR can be calculated using the Pythagoras property as it is also the diagonal of the rectangle PQRS.

$\longmapsto\rm { PR^2 = (5\; km)^2 + (2 \; km)^2}$

$\longmapsto\rm { PR^2 = 25\; km^2 + 4 \; km^2}$

$\longmapsto\rm { PR^2 = 29 \; km^2 }$

$\longmapsto\rm { PR= \sqrt{29 \; km^2} }$

$\longmapsto\bf { PR = \sqrt{29} \; km \; or \; 5.38 \; km}$

∴ The magnitude of the displacement of the person is √29 km or 5.38 km.

$\rule{200}2$

Learn More :

• Distance is the total length of the path covered by the body.
• It is a scalar quantity.
• It is denoted by s.
• Its SI unit is m (metre).
• Displacement is the shortest distance from initial position to final position of the body.
• It is a vector quantity.
• It is denoted by s.
• Its SI unit is m (metre).

Answer 2

Answer:

easy method

step by step