An object experiences two forces acting on the same surface (i.e. they are additive): a force of 5.0N5.0N acting at 60∘60∘ to the horizontal and a force of 8.0N8.0N acting 45∘45∘ to the horizontal.What is the magnitude of the resultant force on the object? Give your answer to the nearest newton, without units.

To find the magnitude of the resultant force, we first need to resolve each force into its horizontal and vertical components.

For the 5.0N force: The horizontal component (Fx1) is 5.0N * cos(60) = 2.5N The vertical component (Fy1) is 5.0N * sin(60) = 4.33N

For the 8.0N force: The horizontal component (Fx2) is 8.0N * cos(45) = 5.66N The vertical component (Fy2) is 8.0N * sin(45) = 5.66N

Next, we add the horizontal and vertical components together to get the total horizontal and vertical forces: Total horizontal force (Fx) = Fx1 + Fx2 = 2.5N + 5.66N = 8.16N Total vertical force (Fy) = Fy1 + Fy2 = 4.33N + 5.66N = 9.99N

Finally, we use Pythagoras' theorem to find the magnitude of the resultant force: Resultant force = sqrt(Fx^2 + Fy^2) = sqrt((8.16N)^2 + (9.99N)^2) = 12.8N

So, the magnitude of the resultant force on the object is approximately 13N (rounded to the nearest newton).