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\noindent {\bf Problem statement} A spaceship maneuvering in space,
far from any gravitational influences, is executing a predetermined
acceleration program which yields a position vector ${\bf r}(t)$ for
the ship, relative to a small space beacon, given by

$${\bf r}(t)=(t-2){\bf i}+(t-3)^2{\bf j}+(t-4)^3{\bf k}.$$ %

\noindent a) Suppose that the captain shuts down the engines at time
$t_0$.  Find the subsequent motion of the ship.

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\noindent b) Show that if $t_0$ is chosen appropriately then the
ship will hit the beacon.









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