A block rests on an inclined plane of angle $\theta$, as shown. Gravity provides a force $\bfF = (0, -m g)$ on the block. (a) What is the component of $\bfF$ in the downhill direction? (b) What is the projection of $\bfF$ in the same direction?
Solution
We begin by drawing the relevant vectors.
We note that $\bfF = (0, -m g)$. A vector pointing downhill as shown is $\bfd = (\cos \theta, - \sin \theta)$.