DUE AT MIDNIGHT PLEASE HELP- Calculus

A trough is 5 meters long, 1 meters wide, and 4 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 4 meters, and base, on top, of length 1 meters). The trough is full of water (density 1000 kg/m3 ). Find the amount of work in joules required to empty the trough by pumping the water out of an outlet that is located 3 meters above the top of the tank. See problem 21, page 464 of the text for a diagram of this trough configuration. (Note: Use g=9.8 m/s2 as the acceleration due to gravity.)

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  1. work = force * distance
    force = gm
    consider thin sheets of water of area 5*(y/4) where y/4 is the width across the tank at depth y

    So, the weight of the sheet of volume dV is 1000kg/m^3 * 9.8N/kg * 5(y/4)dy m^3 = 12250y * dy N

    Work = Int[0,4] 12250y dy
    = 6125 y^2 [0,4]
    = 98000N

    Check my math. . .

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  2. My bad. The water sheet at height y needs to be lifted (4-y)m. Make the fix and recalculate it.

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