Question

To review the solution to a similar problem, consult Interactive Solution 1.43. The magnitude of a force vector is 86.4 newtons (N). The x component of this vector is directed along the +x axis and has a magnitude of 72.3 N. The y component points along the +y axis. (a) Find the angle between and the +x axis. (b) Find the component of along the +y axis.

Answer 1

We have a vector $\vec F$ with a magnitude $F$ of 86.4 N.

a. Let $\theta$ be the angle $\vec F$ makes with the positive $x$-axis. The $x$-component of $\vec F$ is

$F_x=(86.4\cos\theta)\,\mathrm N$

and has a magnitude of 72.3 N, so

$72.3=86.4\cos\theta\implies\cos\theta=0.837\implies\theta=\boxed{33.2^\circ}$

b. The $y$-component of $\vec F$ is

$F_y=(86.4\cos33.2^\circ)\,\mathrm N=\boxed{47.3\,\mathrm N}$