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A man walks 6 km towards the East, then turns right and walks 8 km. How far is he from the starting point?
10 km
12 km
14 km
7 km
10 km
Apply the Pythagoras Theorem (a┬▓ + b┬▓ = c┬▓) to identify the hypotenuse of the right-angled triangle formed by the displacement: sqrt(6┬▓ + 8┬▓) = sqrt(36 + 64) = sqrt(100) = 10.
Apply the Pythagoras Theorem (a┬▓ + b┬▓ = c┬▓) to identify the hypotenuse of the right-angled triangle formed by the displacement: sqrt(6┬▓ + 8┬▓) = sqrt(36 + 64) = sqrt(100) = 10.
Mapping the path
The man travels 6 km East (Base) and turns 90 degrees right to travel 8 km South (Perpendicular). This creates a right-angled triangle where the displacement is the hypotenuse.
Applying Pythagoras Theorem
The shortest distance from the start is calculated using Hypotenuse┬▓ = Base┬▓ + Height┬▓. Plugging in the values: 6┬▓ + 8┬▓ = 36 + 64 = 100. Taking the square root, the distance is 10 km.
B: 12 km is an incorrect sum (6+6) or arbitrary addition; C: 14 km is simply the sum of 6 and 8, which ignores the geometric path; D: 7 km is not mathematically derived from the given displacement vectors.
A is correct because the straight-line displacement between the starting point and the final position forms the hypotenuse of a right-angled triangle with sides 6 and 8, which evaluates to 10 km via the Pythagorean theorem.
Whenever a movement involves a 90-degree turn, immediately look for Pythagorean triplets (like 3-4-5, 6-8-10, 5-12-13) to solve the displacement without manual squaring.