A person walks 27m east and then walks 31m at an angle 38° north of east. What is the magnitude of the total displacement. Answer in units of m
19.08
To find the magnitude of the total displacement, we can use vector addition and the Pythagorean theorem.
First, let’s break down the displacements into their x and y components.
The displacement of 27m to the east would have an x-component of +27m and a y-component of 0m, since it is in the east direction and there is no north or south component.
Next, we need to calculate the x and y components of the second displacement at an angle of 38° north of east.
To find the x-component of this displacement, we use cosine: cos(38°) = adjacent/hypotenuse = x-component/31m.
So, x-component = cos(38°) * 31m = 0.790 * 31m ≈ 24.49m (rounded to 2 decimal places).
To find the y-component of this displacement, we use sine: sin(38°) = opposite/hypotenuse = y-component/31m.
So, y-component = sin(38°) * 31m = 0.624 * 31m ≈ 19.31m (rounded to 2 decimal places).
Now, we have the x and y components for both displacements. We can add them together to get the total displacement.
The x-component of the total displacement = 27m + 24.49m = 51.49m (rounded to 2 decimal places).
The y-component of the total displacement = 0m + 19.31m = 19.31m (rounded to 2 decimal places).
Now, using the Pythagorean theorem, the magnitude of the total displacement is given by the formula: magnitude = sqrt((x-component)^2 + (y-component)^2).
So, magnitude = sqrt((51.49m)^2 + (19.31m)^2) ≈ sqrt(2653.64m^2 + 373.52m^2) ≈ sqrt(3027.16m^2) ≈ 55.01m (rounded to 2 decimal places).
Therefore, the magnitude of the total displacement is approximately 55.01m.