Written homework problem 5
Assigned 9/9 and due 9/15
(This problem was from the first take-home exam when I taught Math 113 in Spring 2011.)
An alien is flying a spacecraft that has no steering controls. The spacecraft is in a parabolic
orbit around a massive star located at (3, 1), and the path of the spacecraft is the curve
y = − 14 (x2 − 6x + 1). The alien starts out at x = 7 and y = −2 and is flying so that her
x-coordinate is decreasing.
The alien wishes to return to her point of origin (namely (0, 0)), and intends to activate the
super powerful engine on the spacecraft. If the engine is activated at the point P , it will shoot
the spacecraft along the line tangent to the parabola at P .
At what point should she activate the engine to return home successfully? Justify your answer
with both words and equations.
1