Orville walks 270 m due east. He then continues walking along a straight line, but in a different direction, and stops 230 m northeast of his starting point. How far did he walk during the second portion of the trip and in what direction?

Please I need a good explanation for this, so there looking for magnitude and direction and I just cant seem to figure it out

The final distance from home is the hypotenuse (230m) of a right triangle with legs 162.63m. Thus, he ends up at point (162.63,162.63).

So, the final leg of his trip is the vector from (270,0) to (162.63,162.63). That is, (-107.37,162.63), which is 194.87m in the direction 123.45 degrees (33.45 deg west of north)

To solve this problem, we can break it down into two parts: the first part when Orville walks 270 m due east, and the second part when he continues walking in a different direction and stops 230 m northeast of his starting point.

Part 1: Orville walks 270 m due east.
Since Orville walks due east, his movement is only in the horizontal direction. Therefore, the magnitude of his displacement in the east direction is 270 m.

Part 2: Orville stops 230 m northeast of his starting point.
To determine the magnitude and direction of Orville's displacement in the second part, we can use the Pythagorean theorem. Let's call the magnitude "d" and the angle formed by Orville's displacement with the north direction "θ".

Using the Pythagorean theorem:
d² = (230 m)² + (230 m)²

d² = 230 m * 230 m + 230 m * 230 m
d² = 53,900 m² + 53,900 m²
d² = 107,800 m²

d = √(107,800 m²)
d ≈ 328.89 m

So, the magnitude of Orville's displacement in the second part is approximately 328.89 m.

To find the direction, we need to determine θ. Since Orville stops northeast of his starting point, θ is the angle formed by the displacement with the north direction. To find this angle, we can use trigonometry.

tan(θ) = opposite / adjacent
tan(θ) = 230 m / 230 m
tan(θ) = 1

θ = arctan(1)
θ ≈ 45°

Therefore, Orville's displacement in the second part of the trip is approximately 328.89 m at an angle of 45° northeast of the starting point.