A man walks 30km east ward and 35km north ward what is the resultant displacement of the man,as well as his direction
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To find the resultant displacement of the man, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the man's path forms a right-angled triangle. The eastward distance of 30km represents one side of the triangle, and the northward distance of 35km represents the other side. Therefore, we can find the resultant displacement by calculating the length of the hypotenuse.
Using the Pythagorean theorem:
Resultant displacement = Square root of (30^2 + 35^2)
Calculating this:
Resultant displacement = Square root of (900 + 1225)
Resultant displacement = Square root of 2125
Resultant displacement ≈ 46.11 km (rounded to two decimal places)
Now let's determine the direction of the resultant displacement. To find this, we can use trigonometry. Specifically, we can use the tangent function:
Tangent of the angle = Opposite side / Adjacent side
In this case, the opposite side is the northward distance (35km), and the adjacent side is the eastward distance (30km).
Tangent of the angle = 35 / 30
Calculating this:
Tangent of the angle ≈ 1.1667
Now we need to find the angle itself. We can use the inverse tangent function (also known as arctangent or atan).
Angle = arctan(1.1667)
Calculating this:
Angle ≈ 49.40 degrees (rounded to two decimal places)
Therefore, the resultant displacement of the man is approximately 46.11 km in the direction of 49.40 degrees (measured counterclockwise from the positive x-axis).