(Solved): A trough has a trapezoidal cross section with a height of 3 \( m \) and horizontal sides of width ...

A trough has a trapezoidal cross section with a height of 3 \( m \) and horizontal sides of width \( \frac{3}{2} \mathrm{~m} \) and \( 3 \mathrm{~m} \). Assume the length of the trough is \( 15 \mathrm{~m} \). See the figure to the right. Complete parts \( (\mathrm{a}) \) and \( (\mathrm{b}) \) 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 \( 1000 \mathrm{~kg} / \mathrm{m}^{3} \) for the density of water and \( 9.8 \mathrm{~m} / \mathrm{s}^{2} \) 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 \( 0 \leq y \leq 3 \), find the cross-sectional area \( A(y) \) in terms of \( y \). \( \mathrm{A}(\mathrm{y})= \) (Simplify your answer. Use integers or fractions for any numbers in the expression.)