Assuming that the drag is proportional to the square of the velocity, one can model the velocity of a falling object as a parachutist, by means of the following differential equation: Where v is the velocity (m/s), t= time (s), g is the acceleration due to gravity (), = second order drag coefficient (kg/m) and m= mass(kg). Solve for the velocity and distance traveled by a 90 kg object with a drag coefficient of 0.225 kg/m. If the initial height is 1 km, determine at what point it hits the ground. Obtain the solution with a) Euler's method b) the method of RK of fourth order
Assuming that the drag is proportional to the square of the velocity, one can model the velocity of a falling object as a parachutist, by means of the following differential equation: Where v is the velocity (m/s), t= time (s), g is the acceleration due to gravity (), = second order drag coefficient (kg/m) and m= mass(kg). Solve for the velocity and distance traveled by a 90 kg object with a drag coefficient of 0.225 kg/m. If the initial height is 1 km, determine at what point it hits the ground. Obtain the solution with a) Euler's method b) the method of RK of fourth order
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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Assuming that the drag is proportional to the square of the velocity, one can model the velocity of a falling object as a parachutist, by means of the following differential equation:
Where v is the velocity (m/s), t= time (s), g is the acceleration due to gravity (), = second order drag coefficient (kg/m) and m= mass(kg). Solve for the velocity and distance traveled by a 90 kg object with a drag coefficient of 0.225 kg/m. If the initial height is 1 km, determine at what point it hits the ground. Obtain the solution with
- a) Euler's method
- b) the method of RK of fourth order
Transcribed Image Text:Assuming that the drag is proportional to the square of the velocity, one can model the velocity of
a falling object as a parachutist, by means of the following differential equation:
dv
dt
= g
m
Where v is the velocity (m/s), t= time (s), g is the acceleration due to gravity (9.81m/s²), ca= second
order drag coefficient (kg/m) and m= mass(kg). Solve for the velocity and distance traveled by a 90
kg object with a drag coefficient of 0.225 kg/m. If the initial height is 1 km, determine at what point
it hits the ground. Obtain the solution with
a) Euler's method
b) the method of RK of fourth order
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