A ball is dropped from the top of a tall building. If air resistance is taken into account, the downward velocity v of the ball is modeled by the differential equation dv = g – kv² dt where g = 9.8 m/sec? is the acceleration due to gravity, and k = 0.1/m is the drag coefficient. Assuming the initial velocity of the ball is zero, use 0.25 sec to estimate the velocity of the ball after one second. Keep track of three I places during the ) Runge-Kutta's method with a step size of calculation. .

A ball is dropped from the top of a tall building. If air resistance is taken into account, the downward velocity v of the ball is modeled by the differential equation dv = g – kv² dt where g = 9.8 m/sec? is the acceleration due to gravity, and k = 0.1/m is the drag coefficient. Assuming the initial velocity of the ball is zero, use 0.25 sec to estimate the velocity of the ball after one second. Keep track of three I places during the ) Runge-Kutta's method with a step size of calculation. .

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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A ball is dropped from the top of a tall building. If air resistance is taken into account, the downward
velocity v of the ball is modeled by the differential equation
dv
= g – kv²
dt
where g = 9.8 m/sec? is the acceleration due to gravity, and k = 0.1/m is the drag coefficient. Assuming
the initial velocity of the ball is zero, use,
0.25 sec to estimate the velocity of the ball after one second. Keep track of three I places during the
b) Runge-Kutta's method with a step size of
calculation. .

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