A man travels a distance of 1.5m towards the East them 2m towards the South and finally 4.5m towards the East in 4 seconds. find the a) total distance travelled b) final displacement?
Answers
TOTAL DISTANCE TRAVELED WILL BE = 1.5 + 2
+ 4.5
=8m
FINAL DISPLACEMENT WILL BE = We can directly make a diagram for 6 m east and 2 m south, the resultant will be same.
Final Displacement = √ ( 6 square + 2 square) √ ( 36 + 4)
= √40 m
ANSWER = (a) 8 m
(b) √40 m
Hope it helps ❤
Solution!!
Given that a man travels a certain distance. We know that total distance is the total length of the path covered by the man.
a) 1.5 m + 2m + 4.5 m
Now, if we add all these measurements then we will get the total distance that the man travelled.
= 8 m
Hence, the total distance covered by the man is 8 m.
b) We have to calculate the final displacement. We know that displacement is the shortest distance from the initial point A to the final point D.
As you can see, I've drawn an imaginary rectangle. The black lines represent the path that the man took. The red line represents the displacement. The blue lines are just to form a rectangle.
The displacement is the diagonal of the rectangle. The breadth of the rectangle is BC and the length of the rectangle is the sum of AB and CD.
Length = 1.5 m + 4.5 m
Length = 6 m
Breadth = 2 m
We can see that a right angled triangle has been formed and the hypotenuse is the diagonal of the rectangle which further is the displacement.
The length and breadth are the base and perpendicular. We will use Pythagoras Theorem to calculate the hypotenuse.
(Base)² + (Perpendicular)² = (Hypotenuse)²
(6 m)² + (2 m)² = (Hypotenuse)²
36 m² + 4 m² = (Hypotenuse)²
40 m² = (Hypotenuse)²
Hypotenuse = √40 m²
Hypotenuse = 2√10 m
Hypotenuse ≈ 6.32 m
Final displacement ≈ 6.32 m
