Homework #1
Due by 5 pm Wednesday September 6th.
Problems from book
- 1-3 This is quite straightforward so long as you visualise the geometry
correctly.
- 1-7 A little trivial vector practice.
- 1-10 Again, simple practice.
- 1-18 Hint, Nguyen pointed out the relationship between cross-products
and triangle areas.
- 1-20 This is practice palying with subscripts.
- 1-22 This is a royal pain and great practice with subscripts.
It is really not hard but it is involved as there are a lot of
cases to cover.
- 1-27 Calculus practice.
- 1-33 More calculus practice.
- 1-36 And still more. Don't forget about the flat surfaces closing the
ends of the cylinder.
- 1-40 You did this in 295, weeek 1. Check the Schaum's Advanced Math book
if you are rusty.
- (Taken from Fowle's book) A fly moves in a spiral path according to the
formula (in Cartesians)
r(t) = (b sin(ωt),b cos(ωt),c t2)
Show that the magnitude of the fly's acceleration is constant (assuming
that b, c, and ω are constant).
- (Courtesy of Seth.) A ball is kicked into the air with an initial speed
of v0 at and angle θ above the horizontal. If there is
no air resistance then the ball follows a parabolic trajectory that you
can all easily find. Derive an expression for the angle φ between the
ground and the radius vector to the ball. Compare the maximum value of φ
with the value of φ when the ball is at the maximum height above the
ground. Would the value of φ at maximum height be the same if you repeated
the computation for a ball on the moon?
