Final answer:
The force due to water pressure on one end of the trapezoidal trough is determined by calculating the hydrostatic pressure at the average depth of the water and multiplying it by the area of the end face of the trough.
Step-by-step explanation:
The student's question relates to calculating the force due to water pressure on one end of a trapezoidal trough filled with water. To approach this problem, we must apply principles from physics, specifically the concepts of pressure and force acting on surfaces submerged in fluids.
The total force exerted by a fluid on a surface is given by the formula F = pghA, where p is the density of the fluid, g is the acceleration due to gravity, h is the depth of the fluid, and A is the area of the surface. Since the question specifies a trapezoidal cross-section and only the base width, top width, and depth are given, we need to assume a vertical end of the trough to calculate the area of this end, which will be a rectangle with the height equal to the water level.
To find the force on one end of the trough, we first calculate the hydrostatic pressure at the average water depth, which is pgh (with h as the average depth since the pressure increases linearly with depth). Then we multiply this pressure by the area in contact with the water, taking into account the submerged height of 3 meters.