B

To calculate the work done by the force, we start with the formula for work:
Work = Force × Displacement × cos(θ)
In this case, the force acting on the body is given by:
$$ F(y) = -2y^2 + 15y + 6 $$
Since the body is constrained to move in the y-direction, we need to evaluate this force at a particular value of y. Assuming the body starts from y=0 and moves to y=10 m, we first calculate the force at y=10 m:
F(10) = -2(10)^2 + 15(10) + 6
F(10) = -200 + 150 + 6 = -44 ext{ N}
The displacement is in the positive y-direction (from 0 to 10 m), and since the force is negative, it acts in the opposite direction to the displacement. Thus, the angle θ = 180 degrees which leads to cos(θ) = -1.
Therefore, the work done is:
Work = F × d × cos(180^{ ext{o}}) = -44 ext{ N} × 10 ext{ m} × (-1) = 440 ext{ J}
Therefore, the work done by the force is 440 J.