A water tank stands on the roof of a building as shown in the figure. The value of height of water above the hole (h) for which the horizontal distance covered by the water (x) is maximum -
A
0.5m
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B
0.8m
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C
1m
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D
0.2m
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Solution
The correct option is C1m We know that speed of efflux is given by, v=√2gh ⇒v=√20h .........(1)
For vertical motion, s=ut+12gt2 4−h=12×10×t2 [ from figure ] t=√4−h5 ...........(2)
For horizontal range of water, x=vt x=√4h(4−h) [ from (1) and (2) ]
On differentiating both side with respect to h dxdh=12(√4h(4−h).(16−8h)
For maximum value of x dxdh=0 ⇒h=2 and h≠0,4
But permitted value of h is from 0 to 1m ∴h=1 for maximum value of x