Resolving Vectors

Resolving vectors means splitting a vector into two component vectors at right angles to each other.The two components are usually horizontal and vertical. Together they have the same effect as the original vector, so they can replace it in calculations.For a vector F at an angle θ to the horizontal:horizontal component F_x = F cosθvertical component F_y = F sinθThe component next to the angle uses cos; the component opposite the angle uses sin.Worked example: a rope pulls a sledge with a force of 50 N at 30° above the horizontal.F_x = 50 cos 30° = 43 NF_y = 50 sin 30° = 25 NOnly the 43 N horizontal component pulls the sledge forwards. The 25 N vertical component partly lifts the sledge, reducing the normal contact force from the ground.Components at right angles are independent: a vertical force has no effect horizontally. This is why resolving is so useful for projectiles and for objects on slopes.To recombine components, use Pythagoras for the size and tan^-1(F_y ÷ F_x) for the angle. Check: √(43.3² + 25²) = 50 N.