Question

A car travels 25 km south, 20 km west, and 15 km north in half an hour. What is the distance travelled and displacement?

Answer 1

Answer:

63.2

Explanation:

1)Total distance travelled  by car is:

15+ 20+45=80km.

2) To show motion of car graphically and calculate displacement :

from the figure displacement is PS

PQ=15KM

QR=20KM

RS=45KM

PS=√PN² +Ns²

√400+3600

63.2km

Hope it helps

Answer 2

The distance traveled by car is 60km

The distance traveled by car is 60km Displacement of the car is 10√5km in the west of southwest direction.

GIVEN

Distance traveled-

25 km south

20 km west

15 km North.

Total Time is taken = 1/2 hour.

TO FIND

Total Distance covered

Displacement of the car.

SOLUTION

We can simply solve the above problem as follows-

Let the car starts its journey from the point, O

So,

OP = 25 km

PQ = 20 km

QR = 15 km

We know that Distance is defined as the total ground an object or a body has covered in a given time frame irrespective of its starting or ending point.

Therefore,

Total distance covered = OP + PQ + QR

= 25 + 20 + 15

= 60 km

We know that displacement refers to the change in the position of the body from its starting to ending position. It is a vector quantity, that is it has both magnitude and direction.

So,

The displacement of the car will be equal to the distance between point 'O' and point 'R'

Let 'S' be the point on OP, such that

RS = PQ = 20 km

QR = SP = 15 km

So,

OP = 25 - 15 = 100km

Now,

Applying the Pythagoras theorem in the right-angled ∆ ORS

${OR}^{2} = {OS}^{2} + {RS}^{2}$

${OR}^{2} = {10}^{2} + {20}^{2}$

${OR}^{2} = 100 + 400$

${OR}^{2} = 500$

OR = √500

OR = 10√5km

displacement = 10√5 km in the west of southwest direction.

Hence,

The distance traveled by car is 60km

The distance traveled by car is 60km Displacement of the car is 10√5km in the west of southwest direction.

( Picture for reference)

#Spj2

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