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Johny starts from Point A and drives 6 km towards the North. He then takes a right turn, drives 17 km, turns right and drives 13 km. He then takes a right turn and drives 8 km. He takes a final right turn, drives 7 km and stops at Point P. How far (shortest distance) and towards which direction should he drive to reach Point A again? (All turns are 90 degrees turns only unless specified.)
9 km towards the East
9 km towards the West
10 km towards the East
10 km towards the West
9 km towards the West
Track the Cartesian coordinates step-by-step from Point A (0,0) to Point P, then calculate the net displacement vector back to Point A.
Track the Cartesian coordinates step-by-step from Point A (0,0) to Point P, then calculate the net displacement vector back to Point A.
Step 1: Trace Movement Leg-by-Leg from Point A (0,0)
Starts at A(0,0), drives 6 km North to (0,6). Takes a right (East) and drives 17 km to (17,6). Takes a right (South) and drives 13 km to (17, -7).
Step 2: Continue Final Turns to Point P
Takes a right (West) and drives 8 km to (9, -7). Takes a final right (North) and drives 7 km, stopping at Point P(9, -7 + 7) = P(9, 0).
Step 3: Calculate Return Direction and Distance to Point A
Point P is at (9, 0) and Point A is at (0, 0). To reach A from P, he needs to cover a horizontal distance of 9 km towards the West.
A: 9 km towards the East would take him further away from Point A. C: 10 km towards the East is incorrect magnitude and direction. D: 10 km towards the West is incorrect magnitude.
B is correct because Point P is located 9 km to the East of Point A, so to reach Point A again, he must drive 9 km towards the West.
Always set the starting point as origin (0, 0) and track horizontal and vertical coordinate shifts independently to avoid visualization errors.
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