The box of groceries placed on an inclined plane can slide down it. The box will slide due to the gravity affecting it, but will be countered by other forces like friction or the normal force.
Along the inclined plane, the gravitational force component parallel with the surface of the incline (the x axis) turns out to be
Fgx = m*g*sin(15)
after some vector trigonometry. The variable 'm' represents the objects mass in kg, 'g' represents the gravitational acceleration on earth, 9.8 m/s2, and the sine of the angle reduces the magnitude of the force proportionally to the angle it is off of the normal, in this case, 15 degrees. To find the acceleration down the plane, in the x direction, it is necessary to sum all forces in the x direction. Part A has us consider this situation in an environment where no friction exists between the inclined plane and the box, thus, there is no resisting force to the x component of the force of gravity, so the sum of forces in the x direction is
∑ Fx : m*g*sin(15) = m*a
setting it equal to 'm*a' allows us to interpret the scenario based on a certain mass, 10 kg. Substituting in known values and canceling out mass because it exists on each side of the equation gives us the new equation:
10*9.8*sin(15) = a
2.536 m/s2 = a, the mass' acceleration down the inclined plane.