MODERN ALCHEMIST

Ripley's Escape from the Nostromo

By now you have a beginning understanding of calculus. It is necessary to apply it to practical problems to make your learning more meaningful.

In the movie Alien, Officer T. Ellen Ripley had approximately 30 seconds from the time she disengaged the escape ship from the Nostromo to the time where the Nostromo exploded.

Previous it was noted that when a function is integrated, a constant appears, but no more was said.

Without the constant, integration provides the function that gives the area under the curve down to zero point on the dependent axis. However, it should not be assumed that the zero point is the point of interest for the calculation. It is for the problem here. More on this later

For the first calculation, assume that the engines provide an acceleration of 9.8 m s^-2, 1 gee.

a(t) = 9.8

We integrate this function with respect to time to determine the velocity function, 9.8t (shown below). Since the velocity at time zero is zero, the constant of integration is zero, and is thus ignored. We now integrate the velocity function with respect to time to provide the distance traveled function. Since distance traveled is zero at time=0, the constant of integration will be zero, and thus ignored.

Thus, distance traveled is 4.9t². You will probably see this equation in physics next year.

After 30 seconds, she has traveled 4410 meters. (4.41 kilometers)

Now, we did the calculation assuming 1 gee of acceleration. My friend Daniel Walker, who is in the air force, says the human body cannot be subjected to much more than 9 gees, and I suspect that is a person with training.

As a homework problem, repeat the above calculation, using an acceleration of 49 m s^-2, which corresponds to 5 gees {9.8 x 5 = 49}.

Final report of the Commercial Starship Nostromo. Third Officer reporting. The other members of the crew, Kane, Lambert, Parker, Brett, Ash and Captain Dallas are dead, the cargo and ship destroyed. I should reach the frontier in about six weeks. With a little luck, the network will pick me up. This is Ripley, last survivor of the Nostromo, signing off.

Previously, we discussing the use of calculus to relate odometer reading (distance) to velocity, we said the odometer started at 000000. However, more than likely, the reading would be something else.

We said that differentiating distance (odometer reading) as a function of time would yield velocity. Recall that differentiation and integration are inverse operations.

differentiating distance yields velocity
integrating velocity yields distance
The constant of integration for the integration of distance vs. time would be the odometer reading at the start of the trip (time=0).

In the above problem we are interested in distance relative to Nostromo. At time=0, the escape ship is at distance=0 relative to the nostromo.

For more in depth information, try the MIT Calculus Index

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