My teacher gave me a homework assignment to try and find themaximum distance of
ID: 1747490 • Letter: M
Question
My teacher gave me a homework assignment to try and find themaximum distance of a golf ball (with lift) can travel.
He gave me 2 different formulas of motion that we are supposedto use to derive our formulas for X and Y.
These formulas are :
-.25Vx - .247Vy = dVx/dt X-direction
and -.25Vy + .247Vx - g =dVy/dt Y-direction
I believe I have to get it to where dVx /Vx for x-direction anddVy/Vy for y-direction but I'm having a hardtime getting them in the right place. Could somebody point mein the right direction?
*******Update*******
The above formula's are the equation's of motion for a spinninggolf ball, and I know I need to Integrate with respect to V and tto get a velocity function, then integrate again to get a poistionfunction in both the x and y directions. But my professor has alsotold the class that we should be using Eurler's Method to solvethis problem because there is no simple analyticsolution.
When I tried to integrate the above formulas all i couldpersonally get was:
X-direction: t = -4ln(-.25Vx-.247Vy)
e^(t/-4) = -.25Vx - .247Vy
Vx = -e^(t/-4) - .247Vy
dx = (-e^(t/-4) - .247Vy)dt
x = -4e^(t/-4) - .247Vy*t
Y-Direction
e^(t/-4) = Vy + .988Vx - g
Vy = -.988Vx - 4g + e^(t/-4)
dy/dx = -.988Vx - 4g + e^(t/-4)
dy = (-.988Vx - 4g + e^(t/-4))dt
y = -.988Vx*t - 4g*t -4e^(t/-4)
And I have tried plugging in small time values (a difference of.01s) and I am getting negative values. I'm not exactly sure how Ishould be applying Euler's Method to this problem, and I'm not sureif my thought process on intergrating these formulas was correct,so I would very greatly appreciate some feed back or direction. Ireally appreciate any and all future/past help on this problem!
Explanation / Answer
-0.25Vx - 0.247Vy = Vx' (1)
-0.25Vy + 0.247Vx - g = Vy' (2)
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