Final answer:
The student's question involves calculating the east and north components of a displacement vector and demonstrating the commutative property of vector addition in the context of a physics problem.
Step-by-step explanation:
The student is seeking assistance with problems involving displacement vectors and their components in a physics context, which is part of high school physics curriculum. In problem 18, you're asked to calculate the distances you would have to drive straight east and then straight north to arrive at the same point if you initially travelled 7.50 km in a direction 15° east of north. Let's solve problem 18. (a) as an example:To find the east (E) component: E = 7.50 km × sin(15°)To find the north (N) component: N = 7.50 km × cos(15°)
(b)To show that reversing the components would still get you to the same location:If you drive the E component (calculated above) and then the N component, it is equivalent to driving on a rectangular path to the initial diagonal displacement. Since the right angle of this rectangle remains consistent, the corner point, which represents your final location, will remain the same. This demonstrates the commutative property of vector addition.