Final answer:
The lady's displacement from her starting point is approximately 541 km at an angle of 56.31° east of north after driving 300 km north and 450 km east.
Step-by-step explanation:
The displacement of the lady from her starting point, after driving 300 km north and then 450 km east, can be calculated using the Pythagorean theorem since the paths create a right-angled triangle. The displacement is the hypotenuse of this triangle, and its magnitude can be found by taking the square root of the sum of the squares of the other two sides:
√(300 km)2 + (450 km)2 = √(90000 + 202500) km2 = √(292500) km2 = 541 km (approx).
The direction of the displacement is given by the angle from the north towards the east. This angle can be calculated using the tangent function:
tangent of the angle = opposite side/adjacent side = 450 km/300 km.
The angle can be found using the inverse tangent function (arctan or tan-1):
angle = arctan(450/300) = arctan(1.5) = 56.31° (approx).
Therefore, the displacement is 541 km at an angle of 56.31° east of north.