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keisanHigh-precision calculations for everyday life and work

Motion Taking Resistance into Account

Author: shiroeExecutions: 6

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Calculates motion taking resistance into account (such as air resistance).
Consider the x-y plane. The x-axis is horizontal, the y-axis is vertical,
the magnitude of gravitational acceleration is g, and the y=-∞ side is defined as “down.”
An object starts at the origin (0,0) with an initial velocity, which we denote as v.
Let θ be the angle at which the object is “thrown.”
We consider cases where “drag” (drag coefficient divided by mass) acts in the opposite direction of velocity and its magnitude is proportional to velocity.
Angle
rad
Initial velocity
m/s
Gravitational acceleration
m/s^2
Resistance Value
1/s
Time step
s
The input range for θ is from 0 to π/2 (in radians).
If t > 0 and y < 0, the calculation is terminated.
The input range for “Resistance” is 0 or greater.
(Resistance coefficient / Mass)

Example value for g: g=9.8
Example time step: 0.1
Example resistance input: 0.7
Example v input: 222
Example θ input: pi/4
(pi/4=90 degrees)

Reference: 1 [m/s] = 360 [m/h]

Reference: 1 [km/h] = 2.777… [m/s]
Reference: 80 [km/h] = 222.222… [m/s]
Reference: 150 [km/h] = 416.666… [m/s]

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