A man walks along the boundary of a square garden at a speed of 2ms-1 . He starts from one corner and returns back to the same place after 2min 40s. Find the length of each side of the garden. How much is his displacement after 80s?
Answers
Given :-
- Total time taken = 2min 40s = 160s
- Displacement after 80s = ?
- Speed of mam = 2m/s
Solution :-
Speed = distance/time
2 m/s = Distance/160
Distance = 320 m
Since it is a square all sides will be equal so ,
Distance of each side = total distance/4 = 320/4 = 80 m
- AB = BD = BC = AC = 80cm
Time taken to travel each side = total time/4 = 160/4 = 40s
✤ Now finding displacement after 80s
Let the square garden be ABCD
So , Time taken to travel :-
- A to B = 40s
- B to D = 40s
♦ A to B + B to D = 80s
♦ A to D = 80s
So we need to find AD = displacement after 80s
✤ Using Pythagoras theorem :-
♦ Hypotenuse² = Base² + Height ²
➜ AD² = AB² + BD²
➜ AD = √80² + 80²
➜ AD = √12800 ≈ 113.13 m
Note :- Refer the attachment to understand more
Conclusion :-
- Length of each side = 80m
- Displacement after 80s ≈ 113.13 m
Answer:
Displacement after 80 sec≈113.137m
Length of each side=80m
Explanation:
Solution:-
Time=2min 40 sec=160sec
Speed=2m/s
Distance=Speed×Time=160×2=320m
As it is a square field
Length of each side=Diameter/4=320/4=80m.
Time taken to cover each side=Distance/4=20 sec
As we know that the side of square are equal so the time taken to cover each side Is equal.
So, Time taken to cover from A to B=40 sec
Time taken to cover from A to D=40 sec
Adding them we get,
A to B+A to D=80 sec
So,the time taken to cover from B To D =80sec
So, By Pythagoras theorem
(Hypotheses)²=The Sum of square of two given sides
(BD)²=AD²+AB²
(BD)²=(80)²+(80)²
(BD)²=6400+6400
(BD)²=12800
BD≈113.137 m
