The figure shows a stream of water flowing through a hole at depth h = 10.2 cm i

Question

The figure shows a stream of water flowing through a hole at depth h = 10.2 cm in a tank holding water to height H = 59.9 cm. (a) At what distance x does the stream strike the floor? (b) At what depth should a second hole be made to give the same value of x? (c) At what depth should a hole be made to maximize x?

The figure shows a stream of water flowing through a hole at depth h = 10.2 cm in a tank holding water to height H = 59.9 cm. (a) At what distance x does the stream strike the floor? (b) At what depth should a second hole be made to give the same value of x? (c) At what depth should a hole be made to maximize x?

Explanation / Answer

apply Bernouliis theorem

as rho gH = rho gh + rho v^2/2

or   gH = gh + v^2/2

so speed V = sqrt(2g(H-h)

V = sqrt(2*9.8 *(0.599-0.102))

V = 3.121 m/s

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part B : Use h = 0.5 gt^2     and x = vt

we get

x = v* sqrt(2h/g)

x = sqrt(2g(H-h)* 2h/g)

x = sqrt(4h(H-h)

x = sqrt(4* 0.102 *(0.599-0.102))

x = 0.202 m    or 20.28 cm

if h = 0.102 m and H-h = 0.599-0.102   = 0.497 m

so secodn hole shouild be made at depth h = 49.7 cm

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x^2 = 4* 0.102 * (0.497)

if x is max, x^2 is also maximum

so

h = H/2 = 59.9/2 = 29.95 cm
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