Homework 3 Due January 30 2007
1) A cannon when stationary is capable of firing a shell in any direction at speed v
0
. This cannon is
mounted on a rocket sled that can accelerate to a speed also equal to v
0
eastwards along an eastwest track.
In this problem we will consider what happens if the cannon is fired from the sled while it is in motion at
top speed (v
0
). We will assume that the recoil effects of the cannon on the sled are negligible. We will also
assume that air resistance and the curvature of the earth are negligible. Use a stationary coordinate system
with origin at the launch point at the firing position of the cannon,
x
axis horizontal eastwards and
y
axis
vertical. Assume the cannon is fired over level ground and the height of the cannon over the ground can be
neglected.
Suppose that the cannon is pointed east and upwards at an angle of
θ
.
a) What is the initial velocity vector of the cannon ball just after it is launched? Give the answer in
component form (i.e. x and y components).
b) What is the velocity vector of the shell as a function of time? Give answer in component form.
c) What is the radius vector (i.e. position vector) of the shell as a function of time in component form?
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 Spring '08
 HerreraSiklody
 Acceleration, Work, Sin, Cos, cannon ball

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