In this homework probelm my teacher assigned, I am given theformulas of motion o

Question

In this homework probelm my teacher assigned, I am given theformulas of motion of a golf ball which include lift in both the xand y directions. From there my professor has stated that there is"no simple analytic solution" and that I must apply Euler's Methodto these equtaions. I'm having a hard time seeing how Euler'sMethod applies. I have tried Integration to get a postion formulafor these problems, but when I apply small times steps to see howfar the ball goes, all I am getting are negative values. Below arethe equations I'm given and the integrated steps I have worked outthus far.
These formulas are : X-direction: -cVx - kVsin(theta) = (mdVx)/dt = -.25Vx -.247Vy = dVx/dt Y-direction: -cVy + kVcos(theta) - mg = (mdVy)/dt= -.25Vy + .247Vx - g = dVy/dt
The ratio of c/m = .25 and the ratio of k/m = .247
The Euler's Formula for the x-direction is Vxi+1 = Ti+1 - Ti [fx (Vxi, Vyi) + Vxi ]    and in the y-direction we get Vyi+1 = Ti+1 - Ti [fy (Vxi, Vyi) + Vyi ]

I really appreciate any and all help on thisproblem! In this homework probelm my teacher assigned, I am given theformulas of motion of a golf ball which include lift in both the xand y directions. From there my professor has stated that there is"no simple analytic solution" and that I must apply Euler's Methodto these equtaions. I'm having a hard time seeing how Euler'sMethod applies. I have tried Integration to get a postion formulafor these problems, but when I apply small times steps to see howfar the ball goes, all I am getting are negative values. Below arethe equations I'm given and the integrated steps I have worked outthus far.
These formulas are : X-direction: -cVx - kVsin(theta) = (mdVx)/dt = -.25Vx -.247Vy = dVx/dt Y-direction: -cVy + kVcos(theta) - mg = (mdVy)/dt= -.25Vy + .247Vx - g = dVy/dt
The ratio of c/m = .25 and the ratio of k/m = .247
The Euler's Formula for the x-direction is Vxi+1 = Ti+1 - Ti [fx (Vxi, Vyi) + Vxi ]    and in the y-direction we get Vyi+1 = Ti+1 - Ti [fy (Vxi, Vyi) + Vyi ]

I really appreciate any and all help on thisproblem!

Explanation / Answer

-0.25Vx - 0.247Vy = Vx' (1)

-0.25Vy + 0.247Vx - g = Vy' (2)   

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