P112 Spring 2007
Homework #9
Due: Friday March 30th, 2007 – At lecture
Reading: 8.48.6
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.
A singlestage rocket is accelerated from rest from
a deepspace platform, where gravity is negligible. If
the rocket burns its fuel in a time of 0.5 s, and the
relative speed of the exhaust gas is 2100 m/s, what
must the mass ration m
0
/m be for a final speed of 8.0
km/s?
2.
A 20.0 kmprojectile is fired at an angle 60.00
above the horizontal and with a speed of 80.0 m/s. At
the highest point of the trajectory the projectile
explodes into two fragments with equal mass, one of
which falls vertically with zero initial speed. Ignore
air resistance. a) How far from the point of firing does
the other fragment strike (level terrain)?
b) how much energy is released during the explosion?
Mathematics Exercises:
3
. Solve the equation sin
2
(y)+sin(2y)=0.
4.
Draw a graph of y = cos
1
(x) for 2
π
<x<2
π
Estimation:
(Marked based solely on logic)
5.
How large would the moon have to be for you to be
able to jump off of it?
Problems:
6.
A helium atom of mass m traveling at an initial
speed v
1
collides
elastically
with an oxygen atom of
mass 4m at rest. The helium atom rebounds from the
oxygen atom at an angle of 90° with respect to its
original direction of motion.
(a) Draw a diagram showing the collision—the
motions of the two particles before and after the
collision. On this diagram, set up xy coordinate
axes, and carefully label the various speeds and
angles that describe these motions.
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 Spring '07
 LECLAIR,A
 mechanics, Solar System, Energy, Work, recitation section number, spring cushion compress

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