A man start from A and walk 3 km eastwards and then 4km southward.what is the displacement or resultant of the man
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Step-by-step solution
3 stepsThis problem involves finding the resultant displacement of two perpendicular movements. We can use the Pythagorean theorem to find the magnitude and trigonometry to find the direction.
Identify the components of displacement.
The man walks 3 km East and 4 km South. These two movements are perpendicular to each other, forming the legs of a right-angled triangle.
Calculate the magnitude of the resultant displacement using the Pythagorean theorem.
The resultant displacement (R) is the hypotenuse of the right-angled triangle.
R² = (Eastward displacement)² + (Southward displacement)²
R² = (3 km)² + (4 km)²
R² = 9 km² + 16 km²
R² = 25 km²
R = √(25 km²)
R = 5 kmCalculate the direction of the resultant displacement.
Let θ be the angle South of East.
tan(θ) = (Opposite side)/(Adjacent side) = (Southward displacement)/(Eastward displacement)
tan(θ) = (4 km)/(3 km)
tan(θ) = 1.333
θ = arctan(1.333)
θ ≈ 53.1° South of EastThe displacement or resultant of the man is 5 km at approximately 53.1° South of East.
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