Page 158 - Data Science Algorithms in a Week

Regression

Therefore, we derived the following formula:

flight_time=0.0008387*distance+1.2335890 hours
Using it, we estimate that the flight from Bratislava to Amsterdam, with the distance 978
km, would take about 0.0008387*978+1.2335890=2.0538376 hours or about 2 hours and 3
minutes, which is a little longer than from Vienna to Amsterdam (1h 55m) and a little
shorter than from Budapest to Amsterdam (2h 10m).

Ballistic flight analysis – non-linear model

An interplanetary spaceship lands on a planet with negligible atmosphere and fires three
projectiles at the same angle carrying exploratory bots, but at different initial velocities.
After the bots land on the surface their distances are measured and the data recorded as
follows:

Velocity in m/s Distance in m

400 38 098
600 85 692
800 152 220

? 300 000
At what speed should the projectile carrying the 4th bot be fired in order for it to land 300
km from the spacecraft?
Analysis:

For this problem we need to understand the trajectory of the projectile. Since the
atmosphere on the explored planet is weak, the trajectory is almost equivalent to the
ballistic curve without the air drag. The distance d traveled by an object fired from a point
on the ground is approximately (neglecting the curving of the planet surface) given by the
equation:

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