A person standing at the centre of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will…
Question and options
A person standing at the centre of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such walks in this pattern?
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Answer and explanation
Correct answer: D - \(\frac{64}{\sqrt{5}}\) meters
Moves: E32, S16, W8, N4, E2, ... Net x = 32-8+2-... = 32/(1+1/4) = 25.6; net y = -(16-4+1-...) = -16/1.25 = -12.8. Distance = sqrt(25.6^2+12.8^2) = 12.8 sqrt5 = 64/sqrt5 m.
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IPMAT Indore
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