A farmer have to go 500 due north, 400 due east and 200 due south to reach his field. If he take 20 min to reach the field. 1)What distance he has to walk to reach the field.2)what is the Displacement from his house to the field.
Answers
the displacement is 500
refer to the image attached for solution....
Answer:
1) 1100 m
2) 500 m
3) 55 m / min
4) 25 m / min
Note:
★ Average speed is given by ;
Total distance covered / Total time taken
★ Average velocity is given by ;
Net development / Total time taken
Solution:
For diagram , please refer to the attachment .
1) Total distance covered by the farmer :
Here,
From figure , it is clear that the total distance covered by the farmer will be ;
= OA + AB + BC
= 500 + 400 + 200
= 1100
Hence,
The total distance covered by the farmer is 1100 m .
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
2) Net displacement of the farmer from house to field :
Also,
The net displacement is OC , which can be obtained by using Pythagoras theorem in ∆OCD .
Thus,
In ∆OCD ,
OC is hypotenuse
OD is base
CD is perpendicular
Thus,
Applying the Pythagoras theorem in ∆OCD , we have ;
=> OC² = OD² + CD²
=> OC² = 400² + 300²
=> OC² = 160000 + 90000
=> OC² = 250000
=> OC = √(250000)
=> OC = 500
Hence,
The net displacement of the farmer is 500 m .
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
3) Average speed of the farmer :
We have ;
Total distance covered = 1100 m
Also,
It is given that , the farmer took 20 mins to reach the field.
Thus,
Total time taken = 20 min
Thus
The average speed of the farmer
Total distance covered
= ------------------------------------
Total time taken
= 1100 m / 20 min
= 55 m / min
Hence,
The average speed of the farmer is 55 m / min .
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
3) Average speed of the farmer :
We have ;
Net displacement = 500 m
Also,
It is given that , the farmer took 20 mins to reach the field.
Thus,
Total time taken = 20 min
Thus
The averag velocity of the farmer
Net displacement
= -----------------------------
Total time taken
= 500 m / 20 min
= 25 m / min
Hence,
The average velocity of the farmer is 25 m / min .
