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![[Post New]](/templates/default/images/icon_minipost_new.gif) 31 Jul 2007 15:46:14 IST
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To a boy cycling at the rate of 4 km/hr eastward , the wind seems to blow directly , from the north . but when he cycles at the rate of 7 km/hr , it seems to blow from from north-east . The magnitude of the actual velocity of the wind is Ans 5 km/hr Please give me a detailed solution ratings sure
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31 Jul 2007 16:18:51 IST
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solution::
using i-j convention of vectors
velocity of boy (v1) = 4i
velocity of rain (V) = x i + y j
(V1rel) velocity of wind with respect to boy = (x i + y j) - 4 i = (x-4)i + y j
but wind blows from north, so (x-4)i = 0
=> x = 4.
new velocity of boy (v2) = 7i
new relative velocity (V2rel) = (4-7)i + y j = -3i + yj
since, now the relative velocity is in north-east direction, so, root((9+y^2)) cos 45 = -3 -->(taken the horizontal component in this step)
solving, you'll get y = 3
=>magnitude velocity of wind is squareroot(16 + 9) = 5 kmph
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