A person runs 5 km North and then turns west and travels for 7 km then turn south for 2 km it takes a person 4 hours to make the

Question

katovenus [111]

3 years ago

6

A person runs 5 km North and then turns west and travels for 7 km then turn south for 2 km it takes a person 4 hours to make the

journey what is the persons distance, speed, displacement and velocity

Physics

1 answer:

Vlad [161] · Answer 1 · 2022-05-21T16:51:57+03:00

1) Distance: 14 km

2) Speed: 3.5 km/h

3) Displacement: 7.6 km at $23.2^{\circ}$ north of west

4) Velocity: 1.9 km/h at $23.2^{\circ}$ north of west

Explanation:

1)

Distance is a scalar quantity, and it corresponds to the total length of the path covered by an object during its motion, regardless of its direction.

Here we have the following motion:

$d_{y1}=5 km$ North

$d_x = 7 km$ west

$d_{y2}=2 km$ south

So, the distance covered is:

$d=d_x + d_y = 5 + 7 +2 = 14 km$

And since it is a scalar, distance has no direction.

2)

Speed is a scalar quantity telling "how fast" an object is moving. It is calculated as:

$speed=\frac{d}{t}$

where:

d is the distance

t is the time taken

In this problem, we have

d = 14 km (distance)

t = 4 h (time taken)

Substituting,

$speed=\frac{14 km}{4 h}=3.5 km/h$

And since it is a scalar, it has no direction.

3)

Displacement is a vector quantity connecting the initial position to the final position of motion. The magnitude is the short distance in a straight line between the initial and final position of motion.

Here we have the following motions:

$d_{y1}=5 km$ North

$d_x = 7 km$ west

$d_{y2}=2 km$ south

So the net displacement in the north-south direction is

$d_y = 5 - 2 = 3 km$ North

$d_x, d_y$ are at right angle, so they form the sides of a right triangle, of which the hypothenuse corresponds to the displacement. Therefore, we can find the magnitude of the displacement by using Pythagorean's theorem: