A cannonball is launched from an initial height of 10 meters with an initial launch angle of 21 degrees and an initial speed of 24 meters/second. We assume the cannonball has a mass of 17.6 kg, diameter of 0.18 meters, a drag coefficient of 0.47 and the density of air is 1.23 kg/m³ as modeled on the PhET simulation lab. (https://phet.colorado.edu/sims/html/projectile- motion/latest/projectile-motion_all.html ) This leads us to a value of μD =0.000418 for the coefficient of drag in the following calculations. Assume acceleration due to gravity is g = 9.8 m/s². Write the system of differential equations that would model the path of the cannonball. Use given values for any constants in the equation. Use Mathematica to compute the maximum height, time of impact and range of the cannonball and confirm your results with the PhET simulator. dv v. dt ᏧᎾ dt = II
A cannonball is launched from an initial height of 10 meters with an initial launch angle of 21 degrees and an initial speed of 24 meters/second. We assume the cannonball has a mass of 17.6 kg, diameter of 0.18 meters, a drag coefficient of 0.47 and the density of air is 1.23 kg/m³ as modeled on the PhET simulation lab. (https://phet.colorado.edu/sims/html/projectile- motion/latest/projectile-motion_all.html ) This leads us to a value of μD =0.000418 for the coefficient of drag in the following calculations. Assume acceleration due to gravity is g = 9.8 m/s². Write the system of differential equations that would model the path of the cannonball. Use given values for any constants in the equation. Use Mathematica to compute the maximum height, time of impact and range of the cannonball and confirm your results with the PhET simulator. dv v. dt ᏧᎾ dt = II
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A cannonball is launched from an initial height of 10 meters
with an initial launch angle of 21 degrees and an initial
speed of 24 meters/second.
We assume the cannonball has a mass of 17.6 kg, diameter
of 0.18 meters, a drag coefficient of 0.47 and the density
of air is 1.23 kg/m³ as modeled on the PhET simulation lab.
(https://phet.colorado.edu/sims/html/projectile-
motion/latest/projectile-motion_all.html )
This leads us to a value of μD =0.000418 for the coefficient
of drag in the following calculations. Assume acceleration
due to gravity is g = 9.8 m/s².
Write the system of differential equations that would model
the path of the cannonball. Use given values for any
constants in the equation.
Use Mathematica to compute the maximum height, time of
impact and range of the cannonball and confirm your
results with the PhET simulator.
dv
v.
dt
ᏧᎾ
dt
=
II
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