P112 Spring 2007
Homework #3
Due: Friday Feb 9th, 2007 – At lecture
Reading: 3.4, 4.14.2, 5.5, 12.1
Not all concepts will be covered in class – you are responsible
for all material in the reading and in the homework problems.
Warmup Exercises:
(Answer only will be marked)
1.
An airplane pilot sets a compass course due west
and maintains an airspeed of 220km/h. After flying
for 0.500h, she finds herself over a town 120 km west
and 20 km south of her starting point.
a) Find the wind velocity (magnitude and direction)
b) If the wind velocity is 40 km/h due south, in what
direction should the pilot set her course to travel due
west? Use the same airspeed of 220 km/h
c) For both parts, (a) and (b), please include carefully
drawn and labeled
velocity vector diagrams
showing
how the airplane's velocity relative to the ground is
related to its velocity relative to the air.
2.
A tennis ball rolls off the edge of the table 0.750 m
above the floor and strikes the floor at a point 1.40 m
horizontally from the edge of the table. You can
ignore air resistance.
a) Find the time of flight,
b) Find the magnitude of the initial velocity
c) Find the magnitude and the direction of the
velocity of the ball just before it strikes the floor.
d) Draw xt, yt, v
x
t and v
y
t graphs for the motion.
Mathematics Exercises:
3.
The coordinates of circular motion of an object
around an origin in the xyplane are given as
functions of time by x(t)= R cos
ω
t and
Y(t)= R sin
ω
t, where R and
ω
are constants.
a)
show that the object’s distance from the origin is
constant and equal to R.
b)
show that at every point the object’s velocity is
perpendicular to its position vector.
c)
Show that the magnitude of the object’s velocity
is constant and equal to R
ω
.
d)
Show that the object’s acceleration is always
opposite in direction to its position vector, and
that the magnitude is R
ω
2
e)
Show that the object’s acceleration has constant
magnitude v
2
/R.
Estimation:
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 Spring '07
 LECLAIR,A
 mechanics, Work, Velocity, recitation section number

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