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A boy is runing on the plane road with v...

A boy is runing on the plane road with velocity v with a long hollow tube in his hand. The water is falling vertically downwards with velocity u. At what angle to the verticaly, he must inclined the tube the water drops enter it without touching its sides ?

Text Solution

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The correct Answer is:
(i) 2s (ii) `10 ms^(-1)` (iii) 5m (iv) `16.25 m` (v) 20 m

(i) `v(t)=(u -g cos 30^(@) t) hat(i) -g sin theta t hat(j)`
From given situation
`u -g cos 30^(@) t = 0`
`t =2 sec`
(ii) Velocity `u_(x) = 0,a_(x) = g cos 30^(@) = (g)/(2)`
`:. v_(x) =0 +(g)/(2) xx 2 = 10 m//s`
(iii) Distance `PO =`
`10 sqrt(3) cos 90^(@) xx t +(1)/(2) xxg sin 30^(@) xx (2)^(2)`
`PO = 10 m :. h = 10 sin 30^(@) = 5 m`
(iv) Maximum height `= h + (u(sin 60^(@))^(2))/(2g)`
`= 5 +((10 sqrt(3) xx (sqrt(3))/(2)))/(20) =16.25 m`
(v) Distance PQ
`OQ = ((10 sqrt(3))^(2))/(2g cos 30^(@))`
`OQ =1 0 sqrt(3)`
`:. PQ = sqrt((PO)^(2) +(O)^(2))`
`= sqrt(10^(2)+(10 sqrt(3))^(2))= 20m`.
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