Final answer:
The distance and direction from Marcus's starting point to the destination can be determined by using trigonometric functions to find the northward and eastward components of his walk and applying the Pythagorean theorem to these components.
Step-by-step explanation:
Marcus and Cody's hiking question involves determining the distance and direction from Marcus's starting point to the destination after Marcus walks 15.0 km at a 30.0 degrees east of north. To solve this problem, we can break down Marcus's walk into northward and eastward components using trigonometric functions. The northward component is found by taking the cosine of 30.0 degrees multiplied by 15.0 km, and the eastward component by taking the sine of 30.0 degrees multiplied by 15.0 km.
Marcus's northward displacement is:
15.0 km × cos(30.0°) = 12.99 km (northward component)
Marcus's eastward displacement is:
15.0 km × sin(30.0°) = 7.5 km (eastward component)
Now, since the destination is 12.0 km due north from their starting point, we can subtract the northward component of Marcus's walk from this distance to find the remaining northward distance to the destination. The remaining northward distance is:
12.0 km - 12.99 km = -0.99 km
The negative sign indicates that Marcus has gone beyond the northward distance to the destination and must now head southward to reach the final spot.
The resultant displacement to the destination from Marcus's current position can be found by using the Pythagorean theorem, considering the remaining northward distance (0.99 km south) and the eastward displacement (7.5 km east).
Therefore, the distance and direction from Marcus's starting point to the destination will require some southward and eastward movement. To get the exact distance and bearing, we would need to calculate the magnitude of the resultant vector and find the angle using appropriate trigonometric functions.