Question

A car travels \(10\) km towards the north, then turns left and covers \(5\) km. After that, it turns right and travels \(8\) km. Finally, the car turns left and covers \(3\) km. In which direction is the car now with respect to the starting point?

• A. North
• B. South
• C. East
• D. West

Hint:

In turning problems, translate each leg into \(x\)- (East/West) and \(y\)- (North/South) changes. Compare magnitudes of the final components to choose the resulting cardinal direction.

Answer 1

The Correct Option is A

Solution:
Step 1 (Set axes).
Let the start be \(O(0,0)\). Take \(+\!y\) as North and \(+\!x\) as East.
Step 2 (Move segment by segment).
1) \(10\) km North: \(P_1(0,10)\).
2) Turn left from North \(\) face West; go \(5\) km: \(P_2(-5,10)\).
3) Turn right from West \(\) face North; go \(8\) km: \(P_3(-5,18)\).
4) Turn left from North \(\) face West; go \(3\) km: \(P_4(-8,18)\).
Step 3 (Net displacement and direction).
From \(O(0,0)\) to \(P_4(-8,18)\): \(8\) km West and \(18\) km North. Since the northward component \((18)\) exceeds the westward component \((8)\), the car is overall to the North of the starting point (specifically, northwest).
\[ {\text{North (Option (a)}} \]