(a) A water trough (pictured below) has a horizontal length of 4 meters and cross sections
perpendicular to the length are equilateral triangles with sides of length 2 meters. The acceleration
due to gravity is 9.8(m)/(s^(2)) and water has a density of 1000k(g)/(m^(3)). Write down an integral which
expresses how much work is required to empty the full trough by pumping the water out through
the top?
(b) How does your answer change if the trough is only filled up to a height of 1m ?
(c) How does your answer change if the water is not only pumped to the top of the tank, but to 2
meters above the top of the tank?
10. (a) A water trough (pictured below) has a horizontal length of 4 meters and cross sections perpendicular to the length are equilateral triangles with sides of length 2 meters. The acceleration due to gravity is 9.8m/s2 and water has a density of 1000kg/m3. Write down an integral which expresses how much work is required to empty the full trough by pumping the water out through the top? (b) How does your answer change if the trough is only filled up to a height of 1m? (c) How does your answer change if the water is not only pumped to the top of the tank, but to 2 meters above the top of the tank?
4m