How Do You Calculate Work and Angle in Vector Problems?

[od943]

Homework Statement

PART A: A force ~F = Fx ˆı+Fy ˆ acts on a particle that
undergoes a displacement of ~s = sx ˆı + sy ˆ
where Fx = 6 N, Fy = −3 N, sx = 5 m, and
sy = 1 m.
Find the work done by the force on the
particle.
Answer in units of J.

PART B: Find the angle between ~F and ~s.
Answer in units of ◦.

PART C: An easy question but still need help:
Which of the following does not involve work?
1. A golf ball is struck.
2. A weight lifter does military presses (lift-
ing weights over his head.)
3. A professor picks up a piece of chalk from
the floor.
4. A runner stretches by pushing against a
wall.
5. A child is pushed on a swing.

Homework Equations

a^2+b^2=c^2
F=ma
W=fcosthetad

The Attempt at a Solution

 

[od943]

so here's my try: i made two triangles...one out of the force vectors and another out of the displacement vectors
i found the resultant displacement vector to be 5^2+1^2=26...so 5.1 m
i found the resultant force vector by doing 3^2+6^2=45...so 6.7 N

if i plug in these numbers into the work equation of W=fdcostheta i'll get W=5.1m*6.7Ncostheta
to find theta i'll do the tantheta=1m/5m or 11.3099 degrees or 348.69 degrees when put in the correct coordinate plane...
so does W=5.1m*6.7Ncos348.69? that equals 33.5 joules.