Question

resolve the force if 100n acting at an angle of 39° with the horizontal in 2 vertical and horizontal components

Answer 1

Task. Resolve the force if $100\mathrm{N}$ acting at an angle of $39{}^{\circ}$ with the horizontal in 2 vertical and horizontal components.

Solution. We assume that the vector $F$ of the force lays in the plane $(x, y)$ so that the $x$ -axis is horizontal and $y$ -axis is vertical. Let $F = (F_x, F_y)$ be the coordinates of its vector. We should find $F_x$ and $F_y$ .

By assumption the length of this vector $|F| = 100 \, \mathrm{N}$ , and the angle with $x$ -axis is $39{}^\circ$ . Therefore,

$$F _ {x} = | F | \cos 3 9 {}^ {\circ} = 1 0 0 * 0. 7 7 7 1 5 = 7 7. 7 1 5 N,$$

and

$$F _ {y} = | F | \sin 3 9 {}^ {\circ} = 1 0 0 * 0. 6 2 9 3 2 = 6 2. 9 3 2 N.$$

Answer. $F_{x} = 77.715 \mathrm{~N}$ , $F_{y} = 62.932 \mathrm{~N}$ .