In 3-5 sentences, describe how you would develop a computational model of the velocity of a satellite based on the current distance from the earth and the time elapsed. Consider the data set given below:

Question

X (distance from earth) 100 20 15 29 67 5
Y (the time elapsed) 31 44 27 22 36 52
If the velocity, V, is given by V=2πXY , find V. Test your code using the trinket tool.

Trinket

Answer 1

To develop a computational model for the velocity of a satellite based on the distance from Earth and the time elapsed, I would use the given formula \( V = 2\pi XY \), where \( X \) represents the distance from Earth and \( Y \) represents the time elapsed. I would first create arrays for both \( X \) and \( Y \) using the provided dataset. Then, I would implement a loop or vectorized operation to calculate the velocity \( V \) for each corresponding pair of \( X \) and \( Y \). Finally, I would visualize the results or print the velocities to analyze the relationship between distance and velocity. This can be executed using programming languages such as Python in the Trinket tool.

Here’s a simple Python code snippet that could achieve this:

import numpy as np

# Constants
pi = np.pi

# Data
X = np.array([100, 20, 15, 29, 67, 5])
Y = np.array([31, 44, 27, 22, 36, 52])

# Velocity calculation
V = 2 * pi * X * Y

# Output the velocities
print(V)

You can run this code in the Trinket tool to test the model and see the computed velocities based on your dataset.