#### Overview of this book

Machine learning applications are highly automated and self-modifying, and continue to improve over time with minimal human intervention, as they learn from the trained data. To address the complex nature of various real-world data problems, specialized machine learning algorithms have been developed. Through algorithmic and statistical analysis, these models can be leveraged to gain new knowledge from existing data as well. Data Science Algorithms in a Week addresses all problems related to accurate and efficient data classification and prediction. Over the course of seven days, you will be introduced to seven algorithms, along with exercises that will help you understand different aspects of machine learning. You will see how to pre-cluster your data to optimize and classify it for large datasets. This book also guides you in predicting data based on existing trends in your dataset. This book covers algorithms such as k-nearest neighbors, Naive Bayes, decision trees, random forest, k-means, regression, and time-series analysis. By the end of this book, you will understand how to choose machine learning algorithms for clustering, classification, and regression and know which is best suited for your problem
Title Page
Packt Upsell
Contributors
Preface
Free Chapter
Classification Using K-Nearest Neighbors
Time Series Analysis
Python Reference
Statistics
Glossary of Algorithms and Methods in Data Science
Other Books You May Enjoy
Index

## Ballistic flight analysis – non-linear model

An interplanetary spaceship lands on a planet with a negligible atmosphere and fires three projectiles carrying exploratory bots at the planet, but at different initial velocities. After the bots land on the surface, their distances are measured and the data is 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 fourth 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 planet is weak, the trajectory is almost equivalent to the ballistic curve without any air drag. The distance, d, traveled by an object fired from a point on the ground, neglecting the curvature of the planet's surface, is given approximately by the following equation:

Where v is the initial velocity of the object, τ is the angle at which the object was fired, and g is the gravitational...