Chapter 14, Problem 071 Your answer is partially correct. Try again. The figure shows a stream of water flowing through a hole at depth h = 11.8 cm in a tank holding water to height H = 54.0 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? 1i IH (a) Number 44.63 (b) Number11.78 (c) Numbe27 UnitsT cm UnitsT cm UnitsT cm
Solution
(b)
x = sqrt(2gh) * sqrt(2(H-h)/g)
x = 2 sqrt(h(H-h))
x\' = 2 sqrt(y(H-y)
When x = x\'
2 sqrt(h(H - h)) = 2 sqrt(y(H-y))
y^2 - Hy + h(H-h) = 0
y = h or (H - h)
Range will be same if the hole is at depth h or H-h
y = 54 – 11.8
y = 42.2 cm
Second hole should be made 42.2 cm deep.
.
Chapter 14- Problem 071 Your answer is partially correct- Try again- T.docx
1. Chapter 14, Problem 071 Your answer is partially correct. Try again. The figure shows a stream
of water flowing through a hole at depth h = 11.8 cm in a tank holding water to height H = 54.0
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? 1i IH (a) Number 44.63 (b) Number11.78 (c) Numbe27 UnitsT cm UnitsT cm UnitsT cm
Solution
(b)
x = sqrt(2gh) * sqrt(2(H-h)/g)
x = 2 sqrt(h(H-h))
x' = 2 sqrt(y(H-y)
When x = x'
2 sqrt(h(H - h)) = 2 sqrt(y(H-y))
y^2 - Hy + h(H-h) = 0
y = h or (H - h)
Range will be same if the hole is at depth h or H-h
y = 54 – 11.8
y = 42.2 cm
Second hole should be made 42.2 cm deep.
