A man walk 3km East and then 4km North what is his resultant displacement? Suppose he walk 3km and 4km 60(degree) North of East. What is the displacement?
5km
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To find the resultant displacement, we can use the Pythagorean theorem to calculate the magnitude of the displacement and trigonometry to determine the direction.
In the first scenario, the man walks 3 km East and then 4 km North. We can visualize this as a right-angled triangle, where the Eastward movement forms the base of the triangle, and the Northward movement forms the height of the triangle.
Applying the Pythagorean theorem, we can calculate the magnitude of the displacement (d):
d = √((3 km)^2 + (4 km)^2)
= √(9 km^2 + 16 km^2)
= √(25 km^2)
= 5 km
So, the magnitude of the resultant displacement is 5 km.
To determine the direction, we can use trigonometry. The angle formed by the Eastward direction and the resultant displacement can be found using the inverse tangent function:
θ = tan^(-1)((Height)/(Base))
= tan^(-1)(4 km / 3 km)
≈ 53.13 degrees
Therefore, the man's resultant displacement is approximately 5 km in magnitude and makes an angle of 53.13 degrees with the Eastward direction.
In the second scenario, where the man walks 3 km and 4 km 60 degrees North of East, we can use a similar approach.
Using trigonometry, we can first find the horizontal component (x) and vertical component (y) of the displacement, and then calculate the magnitude and direction.
The horizontal component (x) can be found using cosine:
x = (3 km) * cos(60 degrees)
= (3 km) * 0.5
= 1.5 km
The vertical component (y) can be found using sine:
y = (4 km) * sin(60 degrees)
= (4 km) * √3/2
= 2√3 km
Applying the Pythagorean theorem, we can calculate the magnitude of the displacement (d):
d = √((1.5 km)^2 + (2√3 km)^2)
= √(2.25 km^2 + 12 km^2)
= √(14.25 km^2)
≈ 3.77 km
To determine the direction, we can once again use trigonometry. The angle formed by the Eastward direction and the resultant displacement can be found using the inverse tangent function:
θ = tan^(-1)((Vertical component)/(Horizontal component))
= tan^(-1)((2√3 km)/(1.5 km))
≈ 56.31 degrees
Therefore, the man's resultant displacement is approximately 3.77 km in magnitude and makes an angle of 56.31 degrees with the Eastward direction.
draw a diagram.
(a) Ever hear of a 3-4-5 right triangle?
(b) for this one, use the law of cosines to find the distance d:
d^2 = 3^2 + 4^2 - 2*3*4*cos(120°)