Answer:
The resultant displacement is 5√2 kilometers.
Step-by-step explanation:
To find the resultant displacement, we can use vector addition. The girl's movement can be represented as two vectors: one going north (5 km) and the other going in the direction of 60 degrees north of east (10 km).
The 5 km north can be represented as a vector in the north direction (0 degrees). So, it has a northward component of 5 km and no eastward component.
The 10 km at 60 degrees north of east can be split into two components: one in the north direction and one in the east direction. To find these components, we can use trigonometry.
The northward component = 10 km * sin(60 degrees) = 10 km * (√3/2) = 5√3 km
The eastward component = 10 km * cos(60 degrees) = 10 km * (1/2) = 5 km
Now, we have two components:
Northward component: 5 km
Eastward component: 5 km (from the 10 km at 60 degrees north of east) + 0 km (from the 5 km due north)
To find the resultant displacement, we can use the Pythagorean theorem because these two components form a right triangle:
Resultant displacement = √(Northward component^2 + Eastward component^2)
Resultant displacement = √(5^2 + 5^2)
Resultant displacement = √(25 + 25)
Resultant displacement = √50
Resultant displacement = 5√2 km
So, the resultant displacement is 5√2 kilometers