A man walks 100m due north and then 150m on a bearing of s30 degree of north.how far and on what bearing is he.from his original position?
not sure what bearing "s30 degree of north" is.
Thanks
I don't know
To find the distance and bearing from the man's original position, we can use vector addition and trigonometry.
Step 1: Convert the bearing to a standard angle.
The bearing of S30° of North can be converted to a standard angle by subtracting it from 90° since the given bearing is measured clockwise from the North. Therefore, the standard angle would be 90° - 30° = 60°.
Step 2: Break down the distances into North and East components.
The man walked 100m due north, so the north component is 100m. For the 150m distance on a bearing of 60°, we need to find the north and east components.
The north component can be found by multiplying the distance by the cosine of the angle: 150m * cos(60°) = 150m * 0.5 = 75m.
The east component can be found by multiplying the distance by the sine of the angle: 150m * sin(60°) = 150m * (√3 / 2) ≈ 129.9m.
Step 3: Add the components to get the displacement.
To find the total north displacement, add the individual north components: 100m + 75m = 175m.
To find the total east displacement, add the individual east components: 0m + 129.9m ≈ 129.9m.
Step 4: Use the components to calculate the distance and bearing.
The distance from the original position is the magnitude of the displacement, which can be found using the Pythagorean theorem:
Displacement = √((total north displacement)^2 + (total east displacement)^2)
Displacement ≈ √((175m)^2 + (129.9m)^2) ≈ √(30625m^2 + 16850.01m^2) ≈ 351.35m
To find the bearing, we need to calculate the angle relative to the North. It can be found using the inverse tangent function:
Bearing = atan(total east displacement / total north displacement)
Bearing ≈ atan(129.9m / 175m) ≈ atan(0.742857) ≈ 36.34°
Therefore, the man is approximately 351.35m away from his original position on a bearing of 36.34° from the North.