Final answer:
The cave explorer's resultant displacement is approximately 19.9 meters at an angle of 25.2° north of east.
Step-by-step explanation:
To find the resultant displacement for the cave explorer who travels 18.0 meters eastward and then 8.50 meters northward, we can use the Pythagorean theorem since this movement creates a right-angle triangle with the two paths as the legs and the resultant displacement as the hypotenuse. First, we calculate the magnitude of the resultant displacement:
- Magnitude (√): √(18.0² + 8.50²) = √(324 + 72.25) = √396.25 = 19.9 meters
To find the direction of the resultant displacement, we need the angle θ with respect to east (assuming east as the 0° direction). This is done by taking the inverse tangent of the northward displacement over the eastward displacement:
- Direction (θ): tan-1(8.50/18.0) = tan-1(0.4722) ≈ 25.2°
The direction is 25.2° north of east. So, the explorer's resultant displacement is approximately 19.9 meters at 25.2° north of east.