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A trough has a trapezoidal cross section with a height of 1 m and horizontal sides of width

`(1)/(2)m`

and 1 m . Assume the length of the trough is 15 m . See the figure to the right. Complete parts (a) and (b) below. a. How much work is required to pump the water out of the trough (to the level of the top of the trough) when it is full? Use

`1000k(g)/(m^(3))`

for the density of water and

`9.8(m)/(s^(2))`

for the acceleration due to gravity. Draw a y-axis in the vertical direction (parallel to gravity) and use the midpoint of the bottom of one edge of the trough as the location of the origin. For

`0<=y<=1`

, find the cross-sectional area

`A(y)`

in terms of

`y`

.

`A(y)=`

(Simplify your answer. Use integers or fractions for any numbers in the expression.)