A man walk 3km East and 4km North what is his resultant displacement? Suppose he walks 3km and 4km 60 degree North of East. What is the displacement?
In first case, displacement is 5 km ( by Pythagoras theorem).
In second case, cosine rule
x^2 = 3^2 + 4^2 - 2*3*4*cos120
x^2 = 25 + 12
x = √37
To find the resultant displacement in both scenarios, we can use the Pythagorean theorem and trigonometry.
In the first scenario where the man walks 3km east and then 4km north, we can create a right triangle with the eastward distance as the base and the northward distance as the height. The resultant displacement can be calculated as the hypotenuse of this right triangle.
Using the Pythagorean theorem, we can find the hypotenuse:
Resultant displacement = √(Eastward distance^2 + Northward distance^2)
= √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5km
Therefore, the resultant displacement is 5km.
In the second scenario where the man walks 3km east and 4km at an angle of 60 degrees north of east, we can use trigonometry to find the resultant displacement.
First, we can find the eastward and northward components of the walk using the given angle and distances. The eastward component will be 3km multiplied by the cosine of 60 degrees, and the northward component will be 4km multiplied by the sine of 60 degrees.
Eastward component = 3km * cos(60°)
= 3km * 0.5
= 1.5km
Northward component = 4km * sin(60°)
= 4km * 0.866
= 3.464km
Now, we can create a right triangle with the eastward component as the base and the northward component as the height. The resultant displacement can again be calculated as the hypotenuse of this right triangle.
Using the Pythagorean theorem, we can find the hypotenuse:
Resultant displacement = √(Eastward component^2 + Northward component^2)
= √(1.5^2 + 3.464^2)
= √(2.25 + 11.985696)
= √14.235696
= 3.77km (rounded to two decimal places)
Therefore, the resultant displacement is approximately 3.77km.