1. A triangular wedge is laid out with vertices at the O(0,0), at B(40cm, 0) and at T(40cm, 30cm). (O, B and T stand for origin, base, and top). Think of the $x$ coordinate as measuring side-to-side motion, and the $y$ coordinate as measuring up-and-down. (The third coordinate will not come into this problem. ) A block of mass $m$ is sitting partway up the wedge.
(a) Find the coordinates of a unit vector that points in the direction from T to O. Call this vector v.
(b) Find the coordinates of a vector perpendicular to the wedge, pointing into the wedge from the mass. Call this vector n.
(c)The force of gravity is F$=-mg$ j, where $g$ is the constant acceleration of gravity (about 32 ft/sec${}^2$, or 9.8 meters/sec${}^2$ --- you can just leave it as $g$). Find the component of F in the v direction, and the component of F in the n direction.
[Physics note: the amount of friction is proportional to the component of F in the n direction, and the friction force points in the v direction, but we're going to ignore friction in this problem.]
(d)Find the vector projection of F in the v direction, and the vector projection of F in the n direction.
(e)To haul the mass up the slope, you need to apply a force in the -v direction that is equal (or greater) than the component of gravity in the v direction. How much work is required to haul the mass up the slope from O to T?
(f)How much work would be required to haul a mass straight up the side of the wedge from B to T?