Your dream job as a 12-ycar-old was to sit at a computer at NASA mission control and guide the motion of the Mars rover across the Martian surface \(2.0 \times 10^{8} \mathrm{~km}\) away. Communication signals to steer the rover travel at the speed of light between Earth and Mars, and the rover's top speed is \(2,0 \mathrm{~m} / \mathrm{min}\). In your dream, your job was to make sure, based on television images beamed back from the craft, that the rover does not run off a Martian cliff. The shift supervisor recommended that your first task be to determine how far ahead in the rover's field of view you have to watch out for obstacles in order to avoid a disaster.